UC-NRLF 


MMfi 


TONS'- 


•I 


M* 

i 


LIBRARY 

OF  THE 

UNIVERSITY-  OF  CALIFORNIA. 

GIFT    OF 


Class 


/ 


ot 
APPLETONS' 

1 1 

SCHOOL  PHYSICS 


EMBRACING    THE    RESULTS    OF    THE    MOST    RECENT 

RESEARCHES  IN  THE  SEVERAL  DEPARTMENTS 

OF  NATURAL  PHILOSOPHY 


BY 

JOHN  D.  QUACKENBOS,  A.  M.,  M.  D.   (LITERARY  EDITOR) 

Professor  of  Rhetoric,  Columbia  College,  New  York 
Member  of  the  N.  Y.  Academy  of  Sciences,  Fellow  of  the  N.  Y.  Academy  of  Medicine 

ALFRED  M.  MAYER,  PH.  D.  SILAS  W.  HOLMAN,  S.  B. 

Professor  of  Physics,  Stevens  Institute  of  Associate  Professor  of  Physics, 

Technology,  Hoboken,  N.  J.  Massachusetts  Institute  of  Technology,  Boston 

FRANCIS  E.  NIPHER,  A.  M.  FRANCIS  B.  CROCKER,  E.  M. 

Professor  of  Physics,  Instructor  in  Electrical  Engineering, 

Washington  University,  St.  Louis,  School  of  Mines,  Columbia  College, 

and  President  St.  Louis  Academy  of  Science  and  President  New  York  Electrical  Society 


NEW  YOKE  •:•  CINCINNATI  •:•  CHICAGO 
AMERICAN    BOOK    COMPANY 


COPYRIGHT,  1891,  BY 
AMERICAN  BOOK  COMPANY. 


ptintefc  b£ 

H>.  Bppteton  &  Company 
J)orft,  -d.  S.  H. 


PREFACE. 


THE  present  volume  is  intended  to  meet  an  existing  demand  for 
a  thoroughly  modern  text-book  on  Natural  Philosophy,  which  shall 
reflect  the  most  advanced  and  practical  laboratory  and  pedagogical 
methods,  and  at  the  same  time  be  adapted,  in  style  and  matter,  for 
use  in  the  higher  grades  of  our  grammar-schools,  our  high-schools,  and 
our  academies.  In  the  belief  that  special  investigators  and  teachers 
are  distinctively  qualified  for  the  purpose,  the  editor  has  assigned  the 
different  sections  of  the  book  to  educators  of  recognized  eminence  and 
skill,  governing  his  selection  in  each  case  by  the  peculiar  qualifica- 
tions of  the  author.  The  reputation  of  the  several  contributors,  and 
the  standing  of  the  great  scientific  schools  which  they  represent,  must 
secure  for  this  work  a  consideration  accorded  to  few  American  school- 
texts.  The  sections  on  motion,  energy,  force,  the  properties  and  con- 
stitution of  matter,  solids,  liquids,  gases,  and  mechanics  proper,  were 
prepared  by  Professor  Silas  W.  Holman,  of  the  Massachusetts  Institute 
of  Technology ;  those  on  heat,  light,  f  rictional  and  voltaic  electricity,  by 
Francis  E.  Nipher,  Professor  of  Physics  in  Washington  University,  St. 
Louis.  Professor  Alfred  M.  Mayer,  of  the  Stevens  Institute  of  Tech- 
nology, Hoboken,  N.  J.,  furnished  the  chapter  on  sound  ;  and  Francis 
B.  Crocker,  E.  M.,  Instructor  in  Electrical  Engineering,  School  of 
Mines,  Columbia  College,  the  sections  relating  to  magnetism  and  the 
practical  applications  of  electricity.  Numerous  friends  of  the  book 
have  aided  the  editor  with  valuable  suggestions  and  criticisms ;  special 
acknowledgment  is  due  to  Professors  Rood,  Trowbridge,  and  "Rees,  of 
Columbia  College,  and  Professor  George  F.  Swain,  of  the  Massachu- 
setts Institute  of  Technology. 

The  attention  of  teachers  is  asked  to  the  following  specific  features  : 
The  thorough  and  original  treatment  of  motion,  energy,  force,  and 
work.  In  the  chapters  on  dynamics,  the  author  has  presented  a  mod- 
ern and  appliable  conception  of  the  nature,  transformation,  and  con- 
servation of  energy,  as  well  as  of  the  relation  existing  between  energy 
and  force.  These  subjects  are  treated  with  the  greatest  simplicity, 

183612 


jv  PREFACE. 

precision,  and  thoroughness,  for  it  is  believed  that  a  proper  under- 
standing of  them  lies  at  the  base  of  all  scientific  knowledge,  however 
far"  it  may  be  pursued. 

The  book  is  adapted  to  students  of  fourteen  years  and  upward,  but 
by  the  occasional  omission  of  an  advanced  paragraph,  an  algebraic 
expression,  or  an  exceptionally  difficult  principle,  the  text  becomes 
perfectly  comprehensible  to  the  most  juvenile  learners.  Thus  it  is  es- 
sentially fitted  to  pupils  of  different  degrees  of  maturity.  The  easier 
principles  may  form  the  basis  of  a  first  year's  course ;  while,  in  the 
second  year,  the  student  will  find  in  the  complete  text  additional  mat- 
ters which  increased  age  and  extended  experience  now  enable  him  to 
grasp  and  appreciate. 

It  has  been  the  aim  of  the  authors  of  this  volume  not  to  teach 
results  merely,  but  to  show  how  these  results  have  been  reached  as 
well  as  what  practical  use  is  made  of  them,  and  thus  to  inspire  the 
learner  with  enthusiasm  in  his  work  of  questioning  Nature.  Prece- 
dence is  everywhere  given  to  the  practical.  The  steam-engine,  the 
electric  motor,  the  telephone,  and  the  telegraph,  even  the  simplest 
tools,  are  shown  to  be  machines  or  devices  by  which  energy  of  some 
form  is  made  to  do  work  useful  to  man.  The  experiments,  especially 
those  described  in  the  chapters  on  dynamics,  etc.,  are  largely  intended 
as  illustrations,  and  not  as  proofs ;  hence  the  pupil  is  not  led  to  draw 
extended  inferences  from  insufficient  evidence — a  habit  antagonistic 
to  proper  and  symmetrical  mental  development.  Further,  the  signifi- 
cance of  the  algebraic  formulae  is  immediately  impressed  upon  the 
learner  by  solved  numerical  examples.  This  feature  is  of  special 
importance  in  the  earlier  discussions,  where  the  abstract  or  general 
statements  are  rendered  much  more  intelligible  because  accompanied 
with  concrete  forms. 

Instructive  diagrams  and  illustrations  have  been  introduced  wher- 
ever it  was  thought  they  would  relieve  the  text ;  suggestive  questions, 
not  intended  to  supersede  minute  examination  by  the  teacher,  but 
rather  to  exercise  the  reasoning  faculties  of  the  pupil,  are  inserted  at 
such  intervals  as  mark  convenient  and  logical  divisions  into  lessons ; 
problems  are  appended  to  the  several  sections,  to  test  the  student's 
understanding  of  the  principles  therein  explained;  and  applications 
of  these  principles  in  every-day  experience  render  them  delightful  to 
learn  and  easy  to  remember. 

The  illustrations  not  only  reproduce  the  more  complicated  appa- 
ratus usually  found  in  the  school  laboratory,  but  also  elucidate  the 
descriptions  of  simple  experiments  that  can  be  successfully  attempted 
by  young  people  with  home-made  appliances.  At  the  beginning  of 


PREFACE.  v 

each  principal  section  is  pictured  a  suggestive  group  of  such  apparatus 
as  will  be  found  necessary  to  the  performance  of  the  experiments  de- 
scribed in  the  chapter  following ;  and,  throughout  the  book,  minute 
instructions  are  given  for  the  cheap  manufacture  of  essential  pieces  of 
apparatus. 

The  publishers  feel  assured  that  the  many  valuable  features  of  this 
new  School  Physics  must  recommend  it  to  teachers  as  a  singularly 
practical  and  authoritative  text-book  on  the  subjects  of  which  it  treats. 

NEW  YORK,  March  2,  1891. 


TABLE   OF   CONTENTS. 


PAGE 

Introduction  and  Preliminary  Definitions      V       .        .        ,  1 

Kinematics        *.-.-... 13 

Energy       .        .        .        .  .        .        .        .        •        •        •     28 

Force 43 

Properties  and  Constitution  of  Matter 60 

Measurement  of  Mass,  Force,  Energy,  and  Work    ....    76 
Action  of  Forces       .        .        .        '.        .        .        ,        .        .        .  105 

Gravitation  and  the  Pendulum 119 

Friction  and  Machines      . •  138 

Three  States  of  Matter .166 

Solids 167 

Liquids 173 

Gases , 200 

Heat 230 

Light 293 

Sound 370 

Magnetism 419 

Electricity 435 

Practical  Applications  of  Electricity 505 


PHYSICS,    OR 
NATURAL    PHILOSOPHY. 


PRELIMINARY  STATEMENTS  AND  DEFINITIONS. 

The  Fundamental  Things  about  which  we  have  to 
learn  in  Physics  are  Matter  and  its  Motion — matter,  out  of 
which  everything  is  built  up ;  motion,  which  gives  to  matter 
the  possibility  of  form,  structure,  phenomena,  and  laws,  and 
which  is  everywhere  and  unceasing. 

Matter  in  motion  possesses  Energy — that  which  not  only 
does  all  the  work  of  the  universe,  but  which  holds  every 
particle  to  its  neighbor  and  yet  keeps  it  apart  from  that 
neighbor. 

Physical  Science  deals  only  with  the  phenomena  and 
laws  of  matter,  and  of  matter  in  motion.  It  does  not  at- 
tempt to  determine  whence  matter  and  its  motion  came, 
what  matter  is,  or  how  it  acquired  motion.  It  does  not 
deny  that  other  things  than  matter  in  motion  are  essential 
to  the  universe.  Whatever  such  things  there  are,  lie  out- 
side the  scope  of  Physical  Science. 

We  are  everywhere  surrounded  by  objects  which  form  a  part  of 
what  we  call  the  physical  universe.  In  studying  them  we  proceed 
upon  the  suppositions  or  beliefs — 

1.  That  they  exist  independently  of  ourselves,  or,  as  we  say,  have 
objective  existence. 

2.  That  we  perceive  them  and  become  acquainted  with  them  solely 
by  the  aid  of  our  senses. 


2  PHYSICS,  OR  NATURAL  PHILOSOPHY. 

3.  That  we  are  liable  to  misinterpret  the  indications  of  our  senses. 

4.  That  the  continued  exercise  of  Reason  enables  us  gradually  to 
sift  the  truth  from  the  error  in  our  interpretation  of  these  indications. 

Phenomena. — As  we  examine  and  consider  the  ob- 
jects about  us,  we  perceive  that  they  differ  as  to  size,  shape, 
color,  hardness,  position,  and  many  other  characteristics  or 
qualities.  We  also  perceive  that  they  are  concerned  in  cer- 
tain events  or  occurrences  which  are  going  on  naturally,  Or 
can  be  made  to  take  place.  Thus,  we  observe  that  objects 
when  dropped  fall  to  the  ground,  that  water  on  a  sloping 
surface  runs  downward,  that  an  object  held  up  in  the  sun- 
shine casts  a  shadow,  that  the  sun  appears  to  rise  in  the 
east  and  set  in  the  west.  These  and  a  multitude  of  other 
events  are  what  we  call  Phenomena. 

Science. — But  a  mere  examination  and  cataloguing 
of  objects  and  phenomena  would  never  give  us  a  science. 
Science  involves  a  study  of  the  relations  between  different 
objects  and  between  phenomena.  These  relations  must  be 
analyzed  and  expressed  in  general  statements,  which  are 
called  Laws.  The  whole  body  of  truth  thus  gained,  namely, 
the  knowledge  of  material  objects,  phenomena,  and  relations 
or  laws,  constitutes  the  science  called  Physics,  or  Natural 
Philosophy. 

Law. — Let  us  look  a  little  more  closely  at  what  is  meant 
by  physical  laws.  If  almost  any  object  whatever  be  held  up 
from  the  earth's  surface  and  then  be  released,  it  will  fall  to 
the  ground.  From  our  own  experience  and  that  of  others 
in  the  past,  we  know  that  every  object  tested  in  this  way 
has  fallen  except  where  for  some  well-understood  cause  it 
was  prevented  from  so  doing,  as,  for  instance,  a  balloon  by 
the  buoyancy  of  the  air  or  a  feather  by  the  resistance  of  the 
air.  We  may,  therefore,  say  that  every  object  tested  has 
shown  a  tendency  to  fall  toward  the  earth. 

But  this  statement  is  merely  a  summary  of  the  facts  or 
phenomena  for  all  bodies  tested,  and  is  not  a  law.  How 


PHYSICAL  LAW.  3 

must  it  be  changed  to  become  one  ?  Simply  by  being  made 
general — that  is,  it  must  be  expressed  so  as  to  apply  to  all 
bodies.  If,  then,  we  say  every  body  near  the  earth  possesses 
a  tendency  to  fall,  that  is,  has  weight,  we  shall  have  a  state- 
ment of  the  class  which  we  call  laws.  This  statement  in- 
cludes every  body  near  the  earth,  whether  it  has  been  tested 
or  not. 

Now,  how  do  we  know  that  this  law  is  true  ?  "We  do  not  know  that 
it  is  true  in  the  same  sense  that  we  know  the  truth  of  the  first  state- 
ment. We  can  not  even  have  the  same  certainty  that  a  given  object 
which  has  weight  to-day  will  have  weight  to-morrow.  How,  then,  can 
we  have  any  confidence  in  general  statements  or  predictions  based 
upon  past  experience  H  And  if  these  laws  are  an  essential  part  ol 
science,  how  much  reliance  is  to  be  placed  upon  them  ?  There  cer- 
tainly is  such  a  thing  as  too  great  confidence  in  science,  and  there  is  a 
wide  difference  between  the  degrees  of  confidence  to  be  given  to  differ- 
ent scientific  laws.  These  laws  are  being  continually  developed  and 
corrected,  and  the  measure  of  confidence  to  which  they  are  entitled 
depends  on  the  thoroughness  with  which  the  underlying  facts  were 
examined,  and  in  the  exactness  with  which  subsequently  observed 
facts  and  phenomena  have  been  found  to  coincide  with  the  law. 

The  chief  reason  why  we  are  disposed  to  put  confidence  in  laws 
and  predictions  is  our  belief  in  the  proposition  that  "  the  same  causes 
will  always  produce  the  same  effects."  This  is  a  generalized  statement 
of  our  own  and  all  past  experience,  viz.,  that  the  same  causes  have 
always  produced  the  same  effects,  and  our  belief  in  it  is  measured  by 
the  breadth  of  experience  upon  which  it  rests. 

It  must  be  remembered  that  laws  do  not  "  govern  "  events 
in  the  sense  of  causing  them.     A  law  is  merely  the  general 
ized  statement  of  what  has  been  observed  to  occur. 

Cause  and  Effect. — What  do  these  terms  mean  ?  Push 
a  book  lying  on  the  table.  It  moves.  Try  the  experiment 
under  a  variety  of  conditions  as  to  time,  place,  temperature, 
and  so  on.  You  will  find  that  the  push,  unless  neutral- 
ized in  some  obvious  way,  always  produces  the  motion,  and 
that  the  motion  does  not  occur  without  a  push.  You  con- 
clude, then,  that  it  appears  not  to  be  simply  a  matter  of 


4  PHYSICS,  OR  NATURAL  PHILOSOPHY. 

chance  that  the  push  and  the  motion  occur  at  the  same 
time,  but  that  they  necessarily  occur  together,  and  that  the 
motion  appears  to  result  from  the  push.  The  push  is  then 
said  to  be  the  cause  of  the  motion,  and  the  motion  the  effect 
of  the  push. 

We  should  feel  a  considerable  degree  of  confidence,  then, 
in  making  the  generalized  statement  that  the  push,  unless 
neutralized,  always  will  produce  the  motion ;  but  we  should 
not  pretend  to  say  that  this  statement  is  absolutely  true,  for, 
besides  the  liability  to  some  imperfection  in  our  observa- 
tions, we  are  not  certain  of  the  truth  of  the  proposition, 
"  the  same  causes  always  produce  the  same  effects  " ;  and 
this  is  an  essential  part  of  the  process  by  which  we  have  ar- 
rived at  the  general  statement. 

In  the  application  of  this  proposition,  we  must  bear  in  mind  that  if 
the  cause  be  not  precisely  the  same  (except  with  respect  to  time),  the 
effect  will  not  be  precisely  the  same ;  it  may  be  extraordinarily  differ- 
ent. For  instance,  a  burnt-out  match  may  be  repeatedly  thrust  into 
gunpowder,  with  always  the  same  effect  of  merely  pushing  aside  the 
grains ;  but,  if  the  match  differs  only  by  being  slightly  hotter  on  some 
occasion,  the  effect  may  be  strikingly  changed. 

Chance. — A  multitude  of  events  which  take  place 
around  us  occur  at  times  or  places  or  in  ways  which,  so  far 
as  we  can  see,  are  without  any  order  or  any  apparent  law  or 
reason.  We  speak  of  such  events  as  occurring  by  Chance ; 
but,  the  more  broad  and  accurate  knowledge  becomes,  the 
more  it  is  evident  that  events  are  orderly  occurrences  and 
capable  of  prediction.  They  appear  to  occur  by  chance, 
only  because  we  do  not  know  their  causes  or  the  laws  which 
represent  their  actions.  With  infinite  knowledge,  all  thought 
of  chance  would  disappear. 

Explanation  of  Phenomena  and  Laws. — A  physical 
phenomenon  or  law  is  said  to  be  explained  or  accounted  for 
when  it  is  shown  to  be  a  particular  case  of  some  more  funda- 
mental law  or  group  of  laws.  By  way  of  illustration,  we 


EXPLANATION  OF  PHENOMENA.         5 

find  that  objects  tend  to  fall  toward  the  earth.  We  ask 
why — that  is,  we  seek  an  explanation.  Sir  Isaac  Newton, 
by  a  study  of  the  motion  of  bodies,  including  that  of  th& 
moon  and  planets,  was  led  to  deduce  the  law  known  as  that 
of  universal  gravitation,  viz.,  that  every  particle  of  matter 
tends  to  approach  every  other  particle,  the  amount  of  the 
tendency  depending  on  the  amount  of  matter  in  the  parti- 
cles and  on  their  distances  apart.  The  tendency  of  objects 
to  fall  toward  the  earth  is,  then,  a  particular  case  of  universal 
gravitation,  and  is  therefore  explained. 

But  we  do  not  know  why  every  particle  tends  to  ap- 
proach every  other — that  is,  we  have  as  yet  no  explanation 
of  universal  gravitation ;  we  do  not  know  any  more  funda- 
mental law  to  which  to  ascribe  it.  Thus  explanation  in  any 
case  only  carries  us  a  step  farther  back;  but  that  step  is 
often  of  great  service.  Without  it,  knowledge  would  be 
fragmentary  and  disconnected. 

Theory. — Hypothesis. — There  are  many  phenomena 
and  laws  which  we  are  not  yet  able  to  show  to  be  special 
cases  of  more  fundamental  known  laws — that  is,  to  explain ; 
but  in  the  effort  to  find  explanations  we  are  continually 
forming  suppositions  and  testing  them  to  see  whether  they 
appear  to  afford  the  explanations  desired.  These  supposi- 
tions in  their  earliest  stages  are  often  very  crude  and  im- 
perfect, and  are  then  called  Hypotheses.  As  they  are  more 
and  more  completely  developed,  and  are  shown  to  be  more 
trustworthy  or  more  probable,  hypotheses  are  called  Theories. 

A  hypothesis  is  developed  into  a  theory  by  continued 
comparison  with  new  facts,  and  by  being  corrected  if  neces- 
sary to  correspond  with  them.  The  theory  is  verified  and 
developed  in  the  same  way,  and  may  eventually  become  so 
well  confirmed  as  to  be  regarded  as  a  highly  probable  law. 

One  of  the  best  tests  of  a  theory  or  law  is  to  predict  what  would 
occur  under  certain  new  conditions  or  at  a  certain  future  time  if  the 
theory  or  law  proves  true,  and  then  to  bring  about  those  conditions  or 


6  PHYSICS,  OR  NATURAL  PHILOSOPHY. 

wait  for  that  time  and  see  whether  the  event  occurs  as  predicted.  If 
it  does,  the  theory  will  be  strengthened.  If  it  does  not,  and  we  can 
show  that  the  prediction  was  correctly  made,  the  theory  is  thereby 
proved  to  be  incorrect  or  incomplete,  and  should  be  amended.  Thus 
the  verification  of  the  prediction  of  eclipses,  of  the  apparently  very 
irregular  path  of  the  moon  among  the  stars,  and  especially  of  the 
existence  of  the  planet  Neptune,  all  based  on  the  law  of  gravitation, 
greatly  strengthens  our  belief  in  that  law. 

Theories  and  even  crude  hypotheses  are  often  of  very  great  service, 
even  when  they  ultimately  prove  to  be  incorrect,  for  they  aid  in  direct- 
ing investigation  and  thus  lead  up  to  truth.  It  is  hardly  to  be  sup- 
posed that  any  theory  now  held  will  eventually  prove  to  be  an  abso- 
lutely correct  expression  of  the  truth  to  which  it  relates ;  but  theories 
are  at  present  none  the  less  indispensable. 

QUESTIONS.— What  are  the  fundamental  things  about  which  we  learn  in  the  study 
of  Physics  ?  Does  physics  have  anything  to  say  as  to  the  origin  of  matter  ? 
of  motion  ?  of  life  ?  What  forms  the  physical  universe  ?  Does  this  universe 
exist  outside  of  our  own  thoughts  ?  How  do  we  perceive  it  ?  What  are  our 
senses  ?  What  enables  us  to  separate  truth  from  error  in  our  observations  f 
Define  qualities  ;  a  phenomenon. 

What  constitutes  the  science  of  Physics  ?  How  does  a  science  differ  from  a 
mere  catalogue  of  facts  and  phenomena  ?  What  has  been  observed  in  regard 
to  the  tendency  of  objects  to  fall  ?  Why  is  this  not  a  law  ?  State  the  law  de- 
rived from  this  observed  fact.  Are  any  physical  laws  supposed  to  be  certainly 
true  ?  Why  ?  For  what  reason  do  we  have  any  confidence  in  them  at  all  ? 

Illustrate  cause  and  effect.  What  do  we  mean  by  saying  that  an  event  occurs 
by  chance  ?  To  a  mind  knowing  everything,  could  there  be  such  a  thing  as 
chance  ?  How,  then,  can  any  one  believe  it  possible  that  the  whole  universe 
exists  as  a  matter  of  chance  ?  What  do  we  mean  by  explanation  ?  Does  ex- 
planation explain  ?  What  is  the  relation  between  theory  and  hypothesis  ? 


DEFINITIONS  CONTINUED. 

Physics,  or  Natural  Philosophy,  is  that  branch  of 
human  knowledge  which  deals  with  all  objects,  phenomena, 
and  Jaws  of  the  material  or  physical  universe. 

In  the  physical  universe  we  come  to  recognize  two,  and 
only  two,  things  which  seem  to  be  indestructible,  and  thus 
to  exist  entirely  independently  of  us  or  of  any  operation  of 
our  senses  or  reason.  These  two  things  are  Matter  and 
Energy.  Hence,  Physics  has  been  also  called  the  science  of 
matter  and  energy. 


THE  IDEA  OF  TIME.  7 

While  physics  neither  denies  nor  affirms  that  there  is 
something  in  the  universe  other  than  matter  and  energy, 
no  complete  discussion  of  such  questions  is  possible  without 
an  adequate  knowledge  of  the  laws  of  this  science. 

Physics,  as  thus  defined,  is  given  its  broadest  scope.  It  includes  al- 
most all  branches  of  science  except  mental  science ;  but  the  term  is 
generally  employed  in  a  much  more  limited  sense.  Those  sciences 
which  deal  with  classification  only  (as  most  of  the  natural  history  sci- 
ences), with  phenomena  where  substances  undergo  changes  in  their 
properties  (chemistry),  or  with  phenomena  which  occur  in  living  be 
ings  (biology) — are  usually  understood  to  be  excluded  when  the  term 
physics  is  employed. 

There  are  also  certain  branches  of  physics  proper  which  are  more 
or  less  distinctly  separated,  or  are  not  usually  treated  in  text-books 
upon  physics.  Such  are  astronomy,  which  deals  with  the  stars,  sui\ 
planets,  nebulae,  comets,  etc.,  their  positions,  motions,  and  laws ;  dy- 
namical geology,  which  treats  of  the  structure  of  the  earth ;  etc. 

The  relations  between  physics,  even  in  the  more  limited  sense,  and 
chemistry  and  biology,  are  extremely  close.  Many  chemical  and  bio- 
logical phenomena  are  almost  purely  physical,  and  this  is  true  to  such 
an  extent  that,  without  a  knowledge  of  a  large  part  of  physics,  little 
progress  can  be  made  either  in  chemistry  or  biology. 

Time. — The  earliest  idea  of  Time  probably  comes  from 
the  recognition  of  the  fact  that  one  event  occurs  after  an- 
other. If  your  memory  were  perfect,  you  could  mentally 
place  all  events  in  your  own  experience  in  the  order  in 
which  they  followed  one  another  in  time ;  but  it  would  be 
impossible  for  you  to  compare  correctly  two  intervals  of 
time  between  different  events.  By  experience,  however,  you 
have  found  that  there  are  certain  natural  processes  which 
appear  to  go  on  in  a  uniform  or  rhythmical  manner,  such  as 
the  succession  of  night  and  day,  of  winter  and  summer,  the 
apparent  motions  of  the  sun,  stars,  and  moon,  the  swings  of 
a  pendulum,  the  flow  of  water  through  an  orifice.  By  re- 
ferring events  to  such  processes,  you  can  arrange  a  system 
by  which  the  order  of  succession  of  all  events  and  the  rela- 
tive intervals  between  them  can  be  expressed. 


8  PHYSICS,  OR  NATURAL  PHILOSOPHY. 

In  the  actual  measurement  of  time,  we  make  use  of  the  period  of 
the  earth's  revolution  around  the  sun  to  mark  the  longer  interval  of  a 
year,  the  rotation  of  the  earth  on  its  axis  to  mark  the  day,  and  the 
beats  of  the  pendulum  to  divide  the  day  into  parts. 

Space. — We  are  accustomed  to  think  of  material  objects 
as  occupying  definite  positions  with  reference  to  one  another 
— that  is,  as  being  at  certain  distances  apart  in  certain  direc- 
tions. We  understand  that  this  is  what  is  meant  when  we 
refer  to  the  relative  positions  of  bodies  in  Space. 

In  thinking  of  the  distance  between  bodies,  we  do  not 
conceive  it  as  depending  upon  any  material  thing  between 
them.  Our  idea  of  their  distance  apart  would  not  be 
changed  if  we  thought  of  them  as  separated  by  no  material 
medium  like  air  or  water.  This  abstract  idea  of  distance, 
or,  as  we  may  express  it,  of  length,  breadth,  and  depth, 
without  any  regard  to  the  presence  of  matter,  forms  the 
basis  of  our  idea  of  space. 

"  Absolute  space  is  conceived  as  remaining  always  similar  to  itself 
and  immovable.  The  arrangements  of  its  parts  can  no  more  be  altered 
than  the  order  of  the  portions  of  time.  To  conceive  them  to  move 
from  their  places  is  to  conceive  a  place  to  move  away  from  itself." 

Relative  Character  of  our  Knowledge  of  Time  and 
Space. — There  is  nothing  to  distinguish  one  portion  of  time 
from  another  except  the  different  events  which  occur  in 
each.  Similarly,  there  is  nothing  to  distinguish  one  part 
of  space  from  another  except  their  relation  to  the  places  of 
material  bodies.  We  can  not  describe  the  time  of  an  event 
without  referring  to  some  other  event,  or  the  place  of  a  body 
except  by  reference  to  some  other  body.  All  our  knowledge 
of  both  time  and  space  is  therefore  essentially  relative. 

Think,  for  instance,  of  our  method  of  stating  the  time  of  an  event. 
We  say  that  something  occurred  in  1776  A.  D.,  on  the  4th  of  July.  We 
mean,  first,  that  it  occurred  after  the  birth  of  Jesus  Christ ;  secondly, 
that  it  occurred  after  that  event  by  an  interval  measured  by  1,776 
whole  revolutions  of  the  earth  about  the  sun  and  by  a  certain  fraction 
of  another  revolution.  Thus  we  ordinarily  reckon  the  time  of  events 


MATTER  DEFINED.  9 

relatively  to  another  (or  standard)  event,  the  birth  of  Christ,  and  by 
means  of  an  event  which  is  being  continually  and  regularly  repeated, 
viz.,  the  revolution  of  the  earth  about  the  sun. 

In  locating  bodies  in  space,  no  such  universal  point  of 
reference  is  used  as  in  time.  Bodies  or  places  upon  or  near 
the  earth's  surface  are  described  as  being  at  a  certain  distance 
in  a  certain  direction  from  any  convenient  starting-point. 

The  exact  location  of  any  point  of  the  earth's  surface  for  precise 
work  in  geod'esy,  geography,  and  astronomy,  is  given  by  latitude,  longi- 
tude, and  height  above  the  sea-level.  Latitude  is  measured  by  angular 
distance  north  or  south  of  the  equator ;  longitude,  by  angular  distance 
east  or  west  from  a  meridian  chosen  at  will,  as  that  passing  through 
Greenwich,  Paris,  or  Washington.  Height  above  the  sea  is  the  ver- 
tical distance  of  the  point  above  the  mean  level  of  the  ocean.  (See. 
Appletons'  Higher  Geography,  page  6 ;  Appletons'  Physical  Geog- 
raphy, page  19.) 

Matter. — On  all  sides  of  us  are -objects,  some  natural, 
some  artificial.  They  are  earth,  water,  and  things  made  of 
wood,  metal,  woolen  and  cotton  fibers,  paper,  stone,  clay, 
etc.  Not  only  can  you  see  these  objects,  but  you-  can  feel 
their  form  by  touch,  and  appreciate  through  the  so-called 
muscular  sense  their  hardness  or  softness,  weight,  etc. 
Many  of  them  can  be  smelled  or  tasted ;  some  can  be  heard 
giving  out  sounds;  others  are  producing  heat,  light,  elec- 
trical and  magnetic  effects.  These  objects  are  made  up  of 
substances  which  are  either  solids  (wood,  metal,  stone,  ice), 
or  liquids  (water,  alcohol),  or  gases  (air,  nitrogen,  oxygen). 
The  only  way  in  which  we  can  learn  about  them,  or  find  out 
that  they  exist,  is  by  means  of  one  or  more  of  our  senses — 
that  is,  through  sight,  touch,  and  the  muscular  sense,  smell, 
taste,  hearing.  Some  of  them  we  can  perceive  in  various 
ways ;  others,  through  only  one  or  two  of  the  senses. 

A  piece  of  brass,  for  instance,  can  be  seen  and  touched,  and  will 

thus  be  found  to  have  color,  shape,  and  hardness ;  if  it  be  smelled,  an 

odor  will  be  detected ;  if  the  tongue  be  touched  to  it,  an  impression 

will  be  made  on  the  nerves  of  taste ;  if  it  be  briskly  struck  against 

2 


10  PHYSICS,  OR  NATURAL  PHILOSOPHY. 

something  hard,  it  will  be  set  into  vibration  and  emit  sound  which  can 
be  heard.  Air,  on  the  other  hand,  is  transparent,  so  that  it  can  not  be 
seen ;  it  can  not  be  perceived  by  the  sense  of  touch  in  the  same  way  as 
a  solid.  But  when  it  is  in  motion  it  is  called  wind,  and  this  we  can 
feel  pressing  against  the  body ;  •  or  when  we  are  moving  through  air 
rapidly,  as  in  running  or  riding,  we  always  experience  its  pressure. 
Pure  air  has  no  odor  or  taste,  but  may  be  set  in  vibration  in  such  a 
way  that  we  hear  sound.  Thus,  air  is  a  material  substance  which  can 
be  perceived  only  by  certain  of  the  senses.  Some  gases,  as  chlorine 
and  iodine,  have  color,  taste,  and  odor.  Study  out  for  yourself  the 
senses  by  which  various  objects  and  substances  about  you  can  be  per- 
ceived—water, salt,  glass,  leather.  What  sense  tells  you  whether  an 
object  is  wet  or  dry  t 

Every  object,  body,  or  substance,  which  can  be 
perceived  through  at  least  one  of  the  senses,  is  a  mate- 
rial object,  body,  or  substance — that  is,  it  is  made  up  of 
Matter.  Matter  is  that  of  which  every  conceivable  sub- 
stance is  composed. 

A  definition  ordinarily  given  is  that  matter  is  anything  which  can 
be  perceived  by  the  senses.  This  definition  will  serve  well  enough  for 
the  present  state  of  your  study.  It  is  objectionable,  because  some  of 
the  sensations  which  we  receive  from  matter  (like  heat)  are  due  to  the 
energy  possessed  by  the  bodies,  and  not  to  the  matter  solely. 

Kinds  of  Matter. — Elements. — Are  all  objects  and 
substances  made  up  of  the  same  kind  of  matter,  or  are  there 
different  kinds  ?  Examination  shows  that  the  substance  of 
which  some  are  composed  appears  very  different  from  that 
of  others.  Chemistry  teaches  that  almost  all  these  sub- 
stances are  compounds — that  is,  they  may,  by  chemical  pro- 
cesses, be  separated  into  substances  which  are  simpler,  and 
these  in  turn  may  be  further  separated.  But  there  is  a  limit 
to  this  process,  for  chemists  find  that  they  soon  arrive  at 
substances  which  can  not  by  any  known  physical  or  chem- 
ical process  be  separated  into  others.  These  are  then  con- 
sidered as  simple  or  elementary  substances,  or  kinds  of  mat- 
ter, and  are  called  the  Elements,  or  the  Chemical  Elements. 
At  present,  there  are  about  seventy  elements  known. 


MASS.— DENSITY.  H 

It  is  possible  that  some  of  the  substances  now  thought  to  be 
elements  may  in  the  future  be  resolved  into  simpler  ones,  and  it  is 
conjectured  that  all  may  eventually  be  shown  to  be  built  up  of  only  a 
single  kind  of  matter. 

Mass,  or  Quantity  of  Matter. — Lift  in  succession  sev- 
eral objects — for  instance,  this  book,  a  stone,  a  glass  of  wa- 
ter, a  chair,  a  bit  of  paper.  Ask  yourself  whether  they  all 
seem  to  contain  the  same  amount  or  quantity  of  matter.  Of 
course,  you  do  not  know  the  process  of  finding  out  how  much 
each  contains,  but  the  objects  are  so  different  in  weight, 
size,  form,  etc.,  that  you  at  once  infer  it  to  be  impossible  for 
them  all  to  contain  equal  quantities  of  matter — and  in  fact 
they  do  not. 

Suppose,  again,  that  from  the  same  stick  of  wood  you 
cut  off  two  pieces,  one  much  larger  than  the  other ;  will  they 
contain  equal  quantities  of  matter?  Obviously  not.  Differ- 
ent objects,  then,  contain  different  quantities  of  matter. 

When  we  wish  to  speak  of  the  quantity  of  matter  con- 
tained in  a  body,  instead  of  using  this  long  phrase,  we  say  its 
Mass.  Mass,  then,  means  merely  quantity  of  matter.  If  an 
object  A  contains  twice  as  great  a  quantity  of  matter  as  an 
object  B,  then  the  mass  of  A  is  twice  the  mass  of  B.  How 
mass  is  measured,  will  be  shown  later. 

Density  may  be  defined  as  the  quantity  of  matter  con- 
tained in  a-  unit  volume  of  any  body  or  substance.  Different 
bodies  may  contain  different  masses  in  the  same  volume, 
and  therefore  have  different  densities. 

If  we  were  to  take  portions  of  equal  volume  (say  a  cubic 
inch)  of  different  substances — lead,  wood,  iron,  air,  water, 
ice — then  these  equal  volumes  would  contain  quite  unequal 
quantities  of  matter.  If  we  had  a  means  of  measuring  these 
quantities  (weighing  will  do  it,  as  will  be  explained),  we 
should  know  the  densities  of  the  different  substances.  The 
ratio  of  the  density  of  any  substance  to  the  density  of  water 
is  called  its  Specific  Gravity.  The  process  of  determination 


12  PHYSICS,  OR  NATURAL  PHILOSOPHY. 

of  density  and  specific  gravity  will  be  treated  more  fully 
hereafter.  Any  body  which  is  of  the  same  density  in  all 
its  parts  is  called  homogeneous. 

Molecules. — All  substances  are  supposed  to  be  consti- 
tuted or  built  up  of  parts  which  are  extremely  minute,  far 
too  small  to  be  seen.  Such  parts  are  called  Mol'ecules.  The 
molecules  of  one  kind  of  substance  are  supposed  to  be 
all  alike,  but  those  of  different  substances  are  diiferent. 
The  single  molecules  are  assumed  to  be  in  turn  built  up  of 
smaller  parts,  which  are  called  Atoms. 

The  molecules  are  supposed  not  to  be  actually  in  contact  as  the 
individual  pellets  would  be  in  a  tumbler  filled  with  shot,  but  to  have 
spaces  between  them  which  are  quite  large  as  compared  with  the  size 
of  the  molecules  themselves.  The  molecules  are  further  believed  to  be 
continually  bounding  to  and  fro  at  great  speed,  striking  against  their 
neighbors,  and  thus  keeping  open  for  themselves  this  space  which  sur- 
rounds them.  These  ideas  and  some  of  the  reasons  for  them  will  be 
more  fully  discussed  farther  on. 

QUESTIONS.— What  does  Physics  include  in  its  broadest  meaning  ?  Why  is  it 
called  the  science  of  matter  and  energy  ?  What  does  Physics  deny  or  affirm 
respecting  the  existence  of  anything  but  matter  and  energy  in  the  universe  ? 
Why  does  Physics  not  enter  into  mental,  moral,  and  religious  questions  ?  Does 
it  deny  the  importance  of  these  questions  ?  How  do  we  arrive  at  our  first  ideas 
of  time  ?  How  is  time  actually  measured  ?  What  is  your  idea  of  space  ?  Why 
are  time  and  space,  as  we  can  know  them,  purely  relative  ?  Illustrate. 

Give  examples  of  matter,  and  explain  how  you  recognize  matter.  Is  water  mat- 
ter ?  Is  air  ?  Are  the  odorous  particles  diffused  through  the  air  when  roses 
are  brought  into  the  room  ?  Can  you  perceive  anything  by  your  senses  which 
is  not  matter  ?  How  is  an  external  world  known  to  us  ?  Of  what  does  touch 
inform  us  ?  Of  the  exact  form,  size,  and  distance  of  bodies.  What  are  ap- 
preciated by  the  muscular  sense  ?  Weight,  resistance,  etc.  On  what  does  this 
sense  to  a  great  extent  depend  ?  On,  the  muscular  nerves.  How  many  senses 
have  you  ?  Enumerate  them,  and  specify  the  part  each  plays  in  revealing  an 
objective  world. 

Define  the  term  Matter.  Are  there  different  kinds  of  matter  ?  How  many  ?  In 
what  way  are  they  discovered  ?  State  your  idea  of  Mass.  Define  and  illustrate 
Density.  Do  we  know  how  matter  is  built  up  ?  How  is  it  supposed  to  be  con- 
stituted ?  What  is  a  molecule  ?  An  atom  ?  Are  molecules  in  contact  ? 


MOTION.  X3 


KINEMATICS. 

MOTION,  ITS  DIRECTION,  VELOCITY,  ACCELERATION, 
AND  COMPOSITION. 

When  we  locate  the  position  or  describe  the  motion 
of  an  object,  we  have  to  consider  the  position  or  motion  of  its 
parts.  It  is  therefore  simpler,  in  first  treating  of  motion, 
to  deal  with  a  material  particle  only,  or  a  portion  of  matter 
so  small  that  for  the  purposes  required  we  need  not  consider 
its  parts,  but  may  treat  it  simply  as  a  whole. 

The  following  paragraphs  contain  definitions  and  propositions 
regarding  mere  motion,  without  any  reference  to  the  bodies  moved, 
or  to  the  forces  or  energy  causing  the  motion,  or  produced  thereby. 
They  really  pertain  to  a  branch  of  pure  mathematics  and  not  of  physics ; 
this  is  called  Kinematics  (kin-e-maf  ics — from  a  Greek  verb  meaning 
to  move).  The  propositions  and  definitions  are  deduced  for  applica- 
tion afterward  to  material  bodies  and  systems. 

Direction. — If  we  draw  any  straight  line  upon  this 
paper,  as,  for  instance,  the  line  A  B,  we  may  think  of  it  as 
having  a  certain  direction.  We  mean  that  it  makes  certain 
angles  with  certain  other  lines,  real  or  imaginary,  to  which 
for  convenience  we  may  choose  to  refer  it. 

For  instance,  the  line  A  B  makes  an  angle  of  thirty  degrees  with 
the  top  edge  of  the  page,  and  another  of  sixty  degrees  with  the  side. 
Direction  is  necessarily  relative  for  the  reason  that 
there  can  be  no  fixed  points  in  space  to  refer  to. 
We  say  that  any  other  line  has  the  same  direction 
as  A  B  when  parallel  to  it.  Thus,  the  direction 
of  a  line  drawn  through  the  point  C  parallel  to  A  B 
would  be  the  same  as  the  direction  of  A  B,  and  vice 
versa.  Any  two  lines  drawn  through  one  point,  and  having  the  same 
direction,  must  of  course  coincide. 

If  a  particle  were  moving  from  A  in  the  direction  of  a  line  A  B,  it 
would  move  along  that  line  so  long  as  it  continued  to  move  in  that 
direction.  If  a  particle  were  at  C,  it  could  mov.e  in  the  direction  of 
A  B  by  moving  in  a  straight  line  through  C,  and  parallel  to  A  B. 


14  KINEMATICS. 

Two  particles  moving  in  parallel  lines  are  thus  said  to  move  in  the 
same  direction.  Two  particles  moving  toward  the  same  point  are  not 
said  to  move  in  the  same  direction  unless  the  point  be  infinitely  distant, 
because  otherwise  they  can  not  be  moving  in  parallel  lines. 

Position. — The  position  of  any  point  A  (Fig.  1)  at  a 
given  instant  of  time  is  said  to  be  known  when  its  distance 
and  direction  from  some  suitable  point  B,  used  for  reference, 
are  known.  To  show  the  direction,  we  may  draw  a  line  from 
B  to  A,  and  state  that  the  direction  is  that  of  this  line  B  A ; 
or  we  may  state  the  angle  which  the  line  B  A  would  make 
with  certain  other  lines  or  planes  used  for  reference. 

Sometimes  we  locate  a  point  by  stating  its  perpendicular  distance 
from  three  reference  planes  at  right  angles  to  one  another.  Thus,  a 
point  in  a  room  may  be  located  by  stating  its  perpendicular  distance 
above  the  floor,  its  distance  from  one  side,  and  its  distance  from  one 
end  of  the  room. 

From  what  has  been  said  regarding  our  idea  of  space  (page  8),  we 
see  that  no  part  of  space  itself  is  different  from  any  other  part,  so  that 
there  is  no  point  in  space  which  we  can  select  as  a  starting-point.  We 
can  not,  therefore,  locate  the  position  of  a  particle  in  space  absolutely. 
All  that  we  can  do  is  to  locate  it  with  reference  to  some  other  particle 
— that  is,  to  locate  it  relatively  by  methods  just  shown. 

Motion  is  Continuous  Change  of  Position. — If  we 

imagine,  for  instance,  a  particle  starting  from  A,  Fig.  2,  and 
B  moving  on  to  A',  we  must  think  of  it  as 

changing  its  position  along  some  line  A  B 


C  A'  (which  we  will  call  its  path),  and  as 
C  occupying  time  in  doing  so.  The  particle 

is  in  motion  only  so  long  as  it  is  continu- 
ously changing  its  position  along  the  path — that  is,  so  long 
as  its  position  at  the  end  of  any  interval  of  time,  however 
short,  is  different  from  that  at  the  beginning.  "We  also 
know  that  the  path  traveled  over  must  be  continuous — that 
is,  can  have  no  gap.  For  a  gap  would  mean  that  the  par- 
ticle was  nowhere  at  that  instant,  which  is  impossible. 

Think  out  some  familiar  examples  of  motion,  and  see  how  what 
you  recognize  as  motion  corresponds  to  the  statements  just  given. 


MOTION.  15 

Note  that  the  object  is  in  motion  only  when  continually  changing  po- 
sition, and  that  position  means  merely  distance  and  direction  from  any 
convenient  object  chosen  for  reference.  Observe  also  that  this  refer- 
ence object  is  selected  without  regard  to  whether  it  is  itself  in  motion 
(as  it  always  is)  or  not,  but  simply  for  convenience. 

Watch  a  ball  moving  through  the  air.  It  is  continuously  chang- 
ing distance  and  direction  from  some  point  on  the  ground.  We  do  not 
in  such  a  case  stop  to  consider  that  the  ground  is  a  part  of  the  earth 
which  is  whirling  on  its  axis  and  around  the  sun.  Suppose  you  are 
standing  still  on  a  car  which  is  moving  slowly  forward.  This  means 
that  the  car  is  continuously  changing  its  position  relatively  to  the 
ground,  but  that  you  are  not  changing  your  position  relatively  to  the 
car.  You  see  at  once  that  relatively  to  the  ground  you  are  in  just  the 
same  motion  as  the  car,  at  the  same  time  that  relatively  to  the  car 
you  are  not  moving.  Thus,  you  are  either  in  motion  or  not  in  motion, 
under  precisely  the  same  actual  conditions,  according  to  the  object  to 
which  you  refer  the  motion.  Similarly,  by  referring  your  motion  to 
a  car  ahead  of  you  which  is  going  faster,  you  say  that  you  are  losing 
on  that  car,  meaning  that  relatively  to  it  you  are  going  backward. 
Hence — 

Motion  is  purely  relative,  both  in  speed  and  direc- 
tion. There  is  no  such  thing  as  absolute  motion,  because 
there  is  no  fixed  point  in  space  (page  9). 

Rest. — When  a  particle  at  a  given  instant  is  not  in  mo- 
tion with  reference  to  some  point  selected  for  convenience, 
the  particle  is  said  to  be  at  rest.  But  at  the  same  instant, 
with  reference  to  some  other  point,  the  particle  is  in  motion ; 
thus,  by  properly  choosing  our  reference  point,  the  motion 
may  be  as  fast  as  we  please,  and  in  any  direction. 

All  that  the  term  Eest  really  means  is  that  relatively  to 
the  chosen  reference-point  the  particle  is  not  changing  posi- 
tion at  the  given  instant.  When  in  every-day  language  we 
speak  of  an  object  at  rest,  we  simply  mean  that  it  is  not 
moving  over  the  surface  upon  which  it  stands. 

Rest,  then,  is  not  a  condition  different  from  motion.  It  is  only 
the  special  case  of  motion  where  the  body  and  reference  point  happen 
to  have  the  same  motion  at  the  same  time.  Whenever,  therefore,  we 
make  a  statement  about  a  body  at  rest,  we  must  not  think  of  it  as  re- 


16  KINEMATICS. 

f erring  to  a  body  absolutely  devoid  of  motion,  or  in  a  condition  differ- 
ing otherwise  than  in  degree  from  that  of  a  moving  body. 

The  Direction  of  Motion  of  a  particle  at  any  given 
instant  is  the  direction  of  its  path  at  that  instant.  If  the 
path  is  a  straight  line,  its  direction  is,  of  course,  that  of  the 
line.  If  the  path  is  curved,  its  direction  at  any  point  is 
that  of  the  tangent  to  the  curve  at  that  point  (a  line  which 
touches  but  does  not  cut  the  curve). 

Let  ABODE  represent  the  path  of  a  moving  particle.  Suppose 
the  part  C  D  of  this  path  to  be  straight.  When  the  particle  is  any- 
where between  C  and  D,  its  direction  of  motion  is 
C  D.  At  any  point  B  of  the  path,  draw  a  tangent 
F  G.  Then  the  direction  of  motion  of  the  parti 
cle  at  B  is  that  of  the  line  F  B  G.  Though  the 
direction  of  the  particle  is  continually  changing 
as  it  passes  B,  we  still  say  that  its  direction  at 
the  instant  when  it  is  at  B  is  F  G.  and  this  is  true 
in  the  same  sense  that  in  geometry  the  tangent 
is  said  to  represent  the  direction  of  the  curve  at  the  point  of  tangency. 
The  path  in  Fig,  3  appears  to  be  all  in  the  plane  of  the  paper,  but 
it  is  meant  to  represent  any  very  crooked  path  not  in  one  plane.  Bend 
a  piece  of  wire,  and  study  out  the  direction  of  motion  of  your  pencil- 
point  as  you  move  it  along  the  wire. 

The  Terms  Uniform  and  Constant  will  be  frequently 
used.  To  some  extent  they  are  employed  to  represent  the 
same  idea,  and  are  therefore  used  interchangeably ;  but  there 
is  a  distinction  to  be  observed  between  them.  We  speak  of 
a  thing  or  quality  as  being  uniform,  implying  that  it  is  the 
same,  wherever  we  are  dealing  with  it.  Thus,  we  speak  of  a 
uniform  surface,  shape,  color,  motion.  A  quantity  is  said 
to  be  constant  if  it  has  the  same  amount  or  value  whenever 
we  meet  it ;  for  example,  a  constant  height,  a  constant  speed. 

Thus  uniform  is  used  mainly  with  reference  to  things  or 
qualities  with  respect  to  place,  and  constant  with  reference 
to  quantities  in  respect  to  time. 

QUESTIONS.— What  is  meant  by  a  material  particle  ?  Why  do  we  deal  with  a  par- 
ticle instead  of  a  body  in  kinematics  ?  Mention  the  subjects  of  kinematics. 
How  do  we  state  the  direction  of  a  line  ?  Can  we  state  the  absolute  direction 


VELOCITY,  OR  RATE  OP  MOTION.        if 

of  a  line  ?  Why  ?  When  do  two  lines  have  the  same  direction  ?  How  can  two 
particles  not  moving  in  the  same  line  move  in  the  same  direction  ?  How  do  we 
define  the  position  of  a  point  ?  Can  we  state  the  absolute  position  of  a  particle 
in  space  ?  Why  ? 

Define  motion.  What  do  we  mean  by  the  path  of  a  moving  particle  ?  Why  must 
the  path  moved  over  by  a  material  particle  be  continuous  ?  Show  how  motion 
is  purely  relative.  If  we  speak  of  a  car  as  moving  along  its  track,  to  what  do 
we  refer  the  motion  ?  Does  this  affirm  anything  about  the  motion  of  the  car 
relatively  to  any  other  object  ?  Is  a  body  at  rest  relatively  to  the  ground  in 
any  different  absolute  condition  with  respect  to  the  sun,  for  example,  than  a 
body  which  is  moving  over  the  ground  ?  Are  we,  then,  to  think  of  rest  as  indi- 
cating anything  whatever  as  to  any  absolute  condition  of  the  body  ?  Is  there 
any  such  thing  as  absolute  rest  or  absolute  motion  ?  Are  we,  then,  to  think  of 
starting  a  body  from  rest  as  any  different  from  making  it  move  faster  when 
already  in  motion  ?  What  do  we  generally  mean  when  we  speak  of  a  body  as 
at  rest  ?  Why  do  we  commonly  refer  motion  or  rest  to  the  ground  ?  If  a  par- 
ticle is  moving  along  a  curved  path,  what  is  its  direction  at  any  given  instant  ? 
What  distinction  is  to  be  observed  between  the  terms  uniform  and  constant  ? 


VELOCITY,   OR  RATE  OF  MOTION. 

The  Veloc'ity  of  a  particle  at  a  given  instant  is  the  rate 
at  which  it  is  moving  at  that  instant.  This  is  also  called  its 
Speed. 

Constant  Velocity,  Uniform  Motion. — If  the  motion 
of  a  particle  is  such  that  in  equal  intervals  of  time,  however 
short,  the  lengths  of  path  traversed  by  it  are  equal,  the 
particle  is  said  to  be  moving  with  a  Constant  Velocity  or 
Uniform  Motion.  The  motion  may,  of  course,  be  over  any 
path,  either  straight  or  curved,  regular  or  irregular.  As  the 
spaces  gone  over  are  equal  for  equal  time  intervals,  it  fol- 
lows that  for  two  such  intervals  the  distance  gone  over 
would  be  twice  as  great  as  for  one ;  for  three,  three  times  as 
great,  etc.  In  other  words,  when  a  particle  moves  with 
constant  velocity,  the  distance  gone  over  in  any  given  time 
is  proportional  to  that  time. 

For  uniform  motion,  the  velocity  is  expressed  by  stating 
the  distance  moved  over  in  a  unit  of  time.  Thus,  velocities 
would  be  stated  as  7  miles  an  hour,  3  feet  a  second,  2  metres 
a  second,  large  units  being  usually  chosen  for  convenience  for 
great  velocities. 


18  KINEMATICS. 

If  we  could  measure  the  actual  distance  passed  over  by  the  particle 
in  one  second,  this  would  evidently  give  its  velocity  directly.  It  is, 
however,  seldom  convenient  to  do  so;  but  we  know  that  the  space 
gone  over  is  proportional  to  the  time  occupied.  Thus,  if  the  particle 
moves  over  3  metres  in  one  second,  it  would  in  0*01  second  move  over 
0-01  of  3  metres  or  0-03  metre.  Conversely,  if  it  moved  over  0*03 

metre  in  0.01  second,  we  know  that  it  would  move  over  7r-—  =  3  metres 

0-01 

in  one  second,  and  the  same  would  be  true,  however  small  the  fraction 
of  a  second.  Hence  we  may  say  that  for  uniform  motion  the  velocity 
is  stated  by  the  ratio  of  the  distance  traveled  to  the  time  occupied. 

In  the  example  just  given  the  velocity  would  be  ^r  =  3  metres  a  sec- 

ond. The  same  velocity  would  have  been  found  if  we  had  measured 
the  space  traveled  in  a  millionth  of  a  second  or  in  a  year.  Thus,  we 
can  find  the  velocity,  even  if  the  particle  does  not  continue  to  move 
for  a  unit  of  time,  but  only  for  a  very  small  fraction  of  a  second,  or 
even  if  the  velocity  is  continually  changing. 

If  a  particle  is  moving  with  a  uniform  velocity  of  7  feet  a  second, 
it  will  in  3  seconds  pass  over  7X3  =  21  feet  ;  in  0*5  second,  over  7  X 
0-5  =  3'5  feet,  and  so  on.  In  general,  if  V  represents  the  velocity  and 
t  the  time  during  which  the  body  moves,  the  space  S,  or  distance  gone 
over  along  the  path,  will  be 

S  =  Vt. 

From  this  it  follows  that  for  uniform  motion  the  velocity  V  (per 
unit  of  time)  is  equal  to  the  space  S  traversed  in  a  given  time  t  di- 
vided by  that  time  —  that  is, 


And  similarly  the  time  t  required  to  travel  a  given  space  S  with  a 
velocity  V  is  found  by  dividing  the  space  by  the  velocity  —  that  is, 


Average  Velocity.  —  If  a  particle  moves  with  a  chang- 
ing velocity  (as,  for  instance,  a  railroad  train  does,  going 
now  faster,  now  slower,  stopping,  and  starting  again),  we 
may  find  it  convenient  to  speak  of  its  average  velocity.  This 
could  be  found  if  we  knew  its  actual  velocity  at  each  in- 
stant, and  then  averaged  all  these  velocities.  The  average 


VELOCITY,  OR  RATE  OF  MOTION.        19 

rr 

velocity,    F,  however,  is  also  given  by  -7,  since  the  train 

would  travel  over  the  same  total  space  S  in  the  same  time  t, 
with  its  actual  changing  velocity,  as  it  would  with  a  uni- 
form velocity. 

Acceleration  is  continual  change  of  velocity.  If  the 
velocity  of  a  particle  is  increasing,  the  acceleration  is  called 
positive,  or  -j-  ;  if  the  velocity  is  diminishing,  minus,  or  — . 
For  convenience,  negative  acceleration  is  generally  called 
retardation,  and  acceleration  is  in  that  case  understood  to 
mean  positive  acceleration.  In  what  follows,  the  term  ac- 
celeration should  be  understood  to  include  both  positive 
and  negative,  unless  otherwise  specified. 

Thus,  if  a  moving  particle  in  successive  equal  intervals  of  time, 
however  short,  passes  over  unequal  distances,  its  motion  and  velocity 
are  no  longer  uniform,  but  are  accelerated.  If  the  spaces  passed  over 
in  successive  equal  intervals  of  time  are  greater  and  greater,  the  veloci- 
ty is  increasing,  and  the  particle  is  receiving"  positive  acceleration ;  if 
they  are  less  and  less,  the  particle  is  receiving  negative  acceleration,  or 
retardation.  Acceleration,  like  position  and  velocity,  and  for  the  same 
reasons,  is  purely  relative.  There  is  no  such  thing  as  absolute  accel- 
eration. 

It  is  very  important  to  remember  that,  if  the  velocity  of 
a  particle  is  in  the  slightest  degree  changed,  acceleration 
must  have  occurred  during  the  change  ;  also,  that  if  a  par- 
ticle has  been  "  set  in  motion,"  it  has  been  accelerated.  The 
rate  at  which  the  velocity  of  the  particle  is  being  changed  is 
known  as  the  Rate  of  Acceleration.  It  is  usually  spoken  of 
as  acceleration  only. 

Constant  Acceleration.  —  Uniformly  Accelerated 
Motion. — If  a  particle  is  moving  along  any  path  in  such  a 
manner  that  its  velocity  is  increased  (or  diminished)  by  equal 
amounts  in  equal  times,  the  acceleration  (or  retardation)  is 
constant,  and  the  motion  is  said  to  be  uniformly  accelerated 


20  KINEMATICS. 

(or  retarded).     If  the  amounts  are  unequal,  the  acceleration 
and  motion  are  variable. 

We  have  a  multitude  of  examples  in  nature  of  accelerated  motion, 
and  a  few  important  ones  of  constant  acceleration.  Any  heavy  body 
allowed  to  fall  freely  toward  the  earth  moves  with  a  uniformly  accel- 
erated motion.  Its  velocity  increases  at  the  rate  of  9!8  metres,  or  32*2 
feet,  a  second. 

Laws  of  Uniformly  Accelerated  Motion. — Let  a  de- 
note the  rate  of  acceleration — that  is,  the  increase  of  velocity 
a  second.  Then,  if  the  particle  starts  from  a  state  of  rest, 
its  velocity  at  the  end  of  one  second  will  be  a  units,  at  the 
end  of  two  seconds  2a  units,  and  so  on.  If  t  =  the  time  in 
seconds  after  starting,  the  velocity  v  at  the  end  of  this  time 

t  will  be 

v  =  at. 

This  law  may  be  expressed  as  follows :  The  velocity  at 
the  end  of  a  time  £,  due  to  the  acceleration,  will  be  equal  to 
the  product  of  the  rate  of  acceleration  and  the  time. 

For  example,  an  object  falling  freely  toward  the  earth  has  an  accel- 
eration a  =  32-2  feet  a  second.  Its  velocity  at  the  end  of  3'5  seconds 
would  then  be  v  =  32-2  x  3'5  =  112'7  feet  a  second. 

The  law  as  to  the  space  traveled  by  a  uniformly  acceler- 
ated particle  may  be  thus  stated :  The  space  s  traveled  in  a 
time  t  is  equal  to  one  half  the  product  of  the  rate  of  accel- 
eration and  the  square  of  the  time,  or  s  =  -j-atf*. 

It  has  just  been  shown  that  the  velocity  at  the  end  of  the  time 
t  will  be  v  =  at.  The  velocity  has  been  increasing  from  zero  at  a  uni- 
form rate;  hence  the  average  velocity  is  \at.  If  the  particle  had  moved 
uniformly  with  this  average  velocity  for  the  same  time  t,  it  would  have 
gone  over  a  distance  \at  x  t  =  ^aP,  and  this  would  have  been  the  same 
as  that  actually  traveled  under  the  accelerated  motion. 

Combined  Uniform  and  Accelerated  Motion. — Sup- 
pose a  particle  moving  with  a  uniform  velocity  F,  to  receive 
an  acceleration  a  in  the  same  direction  as  F,  what  would 
be  its  velocity  at  the  end  of  t  seconds  ?  The  acceleration 
would  of  itself  produce  a  velocity  v  =  at  in  that  time. 


COMPOSITION  OF  MOTIONS.  21 

This  velocity  would  be  added  to  the  other  if  the  acceleration  were 
in  the  direction  of  the  uniform  motion,  and  the  actual  velocity  v'  would 

then  be  V  +  v:  or 

v'  =  V+at. 

If  the  acceleration  were  in  the  opposite  direction  to  the  initial  velocity, 
then  the  actual  velocity  v"  would  be  V—  v,  or 
v"  =  V-  at. 

The  motion  in  the  second  case  would  be  what  is  called  retarded 
motion. 

What  would  be  the  space  traversed  in  the  time  tff  Under  the  uni- 
form motion  alone,  it  would  be  Vt.  Under  the  accelerated  motion,  it 
would  be  one  half  the  product  of  the  rate  of  acceleration  and  the 
square  of  the  time.  If  the  two  motions  were  in  the  same  direction,  the 
space  traversed  would  be  the  sum  of  these.  If  the  motions  were  in 
opposite  directions  (retarded  motion),  the  change  in  position  would  be 
the  difference  of  the  two. 

QUESTIONS.— Define  velocity.  Describe  constant  velocity  and  uniform  motion. 
How  is  the  amount  of  constant  velocity  expressed  ?  How  is  it  measured  ?  De- 
duce the  formula  for  the  space  passed  over  in  a  time  t  with  a  constant  velocity 
V.  If  a  steamer  moving  uniformly  goes  fifty  miles  in  four  hours,  what  is  its 
velocity  ?  If  it  does  not  move  uniformly,  but  stops  several  times,  what  is  its 
average  velocity  ?  If  a  bullet  were  to  start  with  a  velocity  of  one  thousand  feet 
a  second,  how  far  would  it  go  in  three  seconds,  if  it  continued  to  move  uniform- 
ly ?  How  long  would  it  take  to  go  a  mile  ? 

Define  acceleration.  Distinguish  between  acceleration  and  retardation.  Can  ab- 
solute acceleration  be  determined  ?  Why  ?  Does  accelerating  a  body  which  is 
at  rest  differ  in  any  way  from  accelerating  one  which  is  already  in  motion  ?  If 
a  body  is  "  started  "  or  "  set  in  motion  "  from  rest,  is  it  accelerated  in  so  doing  ? 
Describe  constant  acceleration.  Does  retardation  differ  in  nature  from  accel- 
eration ?  Deduce  the  formula  for  uniformly  accelerated  motion  ;  for  combined 
uniform  and  accelerated  motion. 


COMPOSITION  OF  MOTIONS. 

Illustration  of  Composition. — Suppose  that  you  are 
sitting  at  A,  Fig.  4,  in  a  car  moving  uniformly  along,  and 
that  you  are  holding  still  in  your  hand  a  ball.  The  ball  then 
possesses  the  same  onward  velocity  as  the  car  relatively  to 
the  earth,  but  is  at  rest  relatively  to  the  car.  Eoll  the  ball 
straight  across  the  car  to  a  person  sitting  directly  opposite 
to  you,  at  C.  To  do  so  you  would,  of  course,  aim  it  and 
roll  it  just  as  you  would  if  the  car  were  stationary.  You 


22  KINEMATICS. 

know  from  experience  that  it  will  go  across  in  exactly  the 
same  way  in  either  case,  or,  in  other  words,  that  its  motion 
across  the  car  is  independent  of  the  motion  of  the  car  itself 
so  long  as  the  car  is  moving  uniformly. 

The  motion  of  the  ball,  then,  relatively  to  the  car,  is  in 
a  straight  line  at  right  angles  to  the  length  of  the  car.  If 
the  car  is  moving,  then  the  ball  possesses  two  motions,  that 
across  the  car  and  that  of  the  car.  We  will  assume  both  to 
be  with  constant  (but  not  necessarily  the  same)  velocity. 
What,  then,  will  be  the  actual  motion  of  the  ball  relatively 
to  the  ground  or  track,  as,  for  instance,  you  might  see  it  if 
you  were  standing  in  the  street  ? 

If  you  think  carefully  you  will  see  that  it  will  move  along  a  diag- 
onal line  such  as  A  C' ;  for,  while  rolling  toward  the  opposite  side  C  of 

the  car,  the  ball  and 
C'__  car   are  moving  on- 

ward, so  that  C  is  ap- 
proaching C'.  When 
the  ball  has  reached 
the  opposite  point  of 
FIG.  4.— COMPOSITION  OF  MOTION.  the  car,  that  point 

will  have  arrived  at 

C'.  Hence  the  ball  must  have  been  traveling  actually  over  the  diag- 
onal line  A  C'. 

This  is  a  single  example  of  a  multitude  of  such  combinations  of 
different  motions  which  are  continually  occurring  about  us  at  every 
instant.  It  is  essential  to  see  how  we  may  study  out  such  cases.  We 
will  take  this  up,  then,  as  a  study  of  pure  motion. 

Resultant  of  Two  Uniform  Motions. — Suppose  a  free 
particle  to  be  moving  with  a  uniform  velocity  along  a  straight 
line  ABC,  and  at  any  moment,  as  when  it  is  at  B,  another 
motion  to  be  imparted  to  it  which,  if  the  first  motion  did 
not  exist,  would  give  it  a  uniform  velocity  in  the  direction 
B  D.  What  will  be  the  resulting  actual  motion  ?  It  is 
found  from  all  experience  that  the  particle  will  in  any  given 
time  have  moved  just  as  far  away  from  the  line  A  C  as  it 
would  have  moved  along  B  D  if  the  first  motion  had  not  ex- 


COMPOSITION  OF  MOTIONS.  23 

isted.  The  actual  position  of  the  particle  will  not  be  along 
either  B  D  or  B  C  ;  but  it  will  have  moved  as  far  from  the 
line  B  D  as  if  only  the  first  motion  had  existed,  and  as  far 
from  the  line  B  C  as  if  only  the  second  motion  had  existed. 

To  state  the  case  a  little  more  completely,  we  must  remember  that 
any  two  lines  have  the  same  direction  when  they  are  parallel.    Then, 
at  any  given  instant  after  leaving  B 
with  both  motions,  say  when  it  has  D/ 

reached  e,  the  change  of  position  of  the  / 

particle,  measured  in  the  direction  of  / 

B  C,  will  be  d  e,  and  in  the  direction  /  / 

of  B  D  will  be  c  e.     The  actual  mo-       / / 

tiori  of  the  body,  relatively  to  any  point       A       B  c      C 

fixed  on  A  C,  is  neither  along  A  C  nor        FIG.  5.— RESULTANT  MOTION. 
B  D,  but  along  some  line  which  is  found 

by  experiment,  and  which  will  presently  be  shown  to  be  the  straight 
line  joining  B  with  e.  The  actual  motion  is  called  the  resultant 
motion,  and  the  actual  velocity  the  resultant  velocity. 

If,  then,  a  particle  be  simultaneously  affected  by  two  or 
more  motions,  the  amount  of  change  of  position  produced 
in  a  given  time  by  each  motion,  measured  in  its  own  direc- 
tion, is  as  great  as  if  no  other  motion  were  present. 

The  process  of  combining  motions  is  called  Composition 
of  Motions,  and  will  now  be  described. 

,  Parallelogram  of  Motions. — Suppose  a  particle  at  A, 
Fig.  6,  to  be  given  simultaneously  two  such  uniform  motions 
in  straight  lines  that  in  equal  times  the  motions  acting  sep- 
arately would  bring  the  particle  to  B  and  to  C.  If  they  act 
together,  the  first  would  change  the  position  of  the  particle 
by  a  distance  equal  to  A  B,  measured  parallel  to  A  B  and  from 
the  line  A  C ;  the  second  would  change  the  position  by  an 
amount  equal  to  A  C,  parallel  to  it,  and  measured  from  A  B. 
Draw  the  lines  C  D  and  B  D,  parallel  to  A  B  and  A  C  re- 
spectively. This  will  complete  the  parallelogram  A  B  D  C. 
Then  D  will  be  the  actual  position  of  the  particle  at  the  end 
of  the  time. 


24  KINEMATICS. 

Subdivide  the  line  A  B  into  any  number  of  equal  parts  at  .E,  F,  G, 
etc.,  and  the  line  A  C  into  an  equal  number  at  H,  I,  J,  etc.  Then,  as 

the  motion  is  uniform, 
rD  the  spaces  A  E,  E  F, 
FG,  GB,  AH,  HI, 
etc.,  will  be  passed 
over  in  equal  times. 
Hence,  at  the  end  of 

c  Q  the  first  of  these  in- 

FIG  ^-PARALLELOGRAM  OF  MOTIONS.  tervals,    the    particle 

must  be  at  K,  formed 

by  completing  the  parallelogram  A  E  K  H.  At  the  end  of  the  second, 
the  particle  must  be  at  L,  similarly  formed,  etc.  Hence,  the  particle 
in  its  actual  motion  must  pass  along  the  line  A  D,  the  diagonal  of  the 
parallelogram. 

If  a  particle  be  simultaneously  given  two  uniform  mo- 
tions, we  may  find  the  resultant  motion  as  follows :  Draw 
through  a  point  lines  parallel  to  the  direction  of  the  two 
separate  motions.  Lay  off  on  these  lines  lengths  propor- 
tional to  the  spaces  over  which  the  particle  would  move  in 
equal  times.  Complete  the  parallelogram  and  draw  the 
diagonal  from  the  starting-point.  The  particle  would  then 
move  along  this  diagonal  at  a  uniform  rate,  and  in  the  same 
time  that  it  would  move  over  either  side.  The  diagonal  is 
then  said  to  represent  the  resultant  motion  in  direction  and 
amount. 

A  person  rowing  a  boat  across  a  stream  flowing  with  a  rapid  cur- 
rent, and  heading  always  at  right  angles  to  the  shore,  will  reach  the 
farther  bank  far  below  the  point  opposite  to  which  he  started.  The 
resultant  motion  will  be  diagonally  across  the  stream,  being  com- 
pounded of  the  forward  motion  of  the  boat  and  the  downward  motion 
of  the  stream,  which  carries  the  boat  with  it.  Similarly,  a  sail-boat 
with  a  side-wind  does  not  reach  the  point  it  heads  for,  because  the  boat 
drifts  sidewise  with  the  wind,  besides  moving  forward.  This  sidewise 
motion  is  called  leeway.  The  resultant  motion  is  therefore  diagonal, 
and  not  straight  ahead.  In  both  cases,  allowance  for  leeway  has  to  be 
made  by  pointing  the  boat,  if  possible,  enough  farther  up-stream,  or 
into  the  wind,  to  cause  the  resultant  motion  to  have  the  direction  in 
which  it  is  desired  to  move  the  boat. 


COMPOSITION  OF  MOTIONS. 


25 


Resultant  of  Several  Uniform  Motions. — If  a  particle 
be  simultaneously  given  more  than  two  uniform  motions  in 
the  same  plane,  we  may  find  the  resultant  of  them  all  by  first 
combining  any  two ;  then  their  resultant  with  a  third ;  etc. 

Let  a  b,  ac,  ad,ae  represent  in  amount  and  direction  the  separate 
motions.  From  any  point  A  draw  A  B  equal  and  parallel  to  a  b ;  B  C 


FIG.  7.— RESULTANT  OF  A  NUMBER  OF  UNIFORM  MOTIONS. 

equal  and  parallel  to  ac:  CD,  to  ad',  and'DE,  to  ae.    Then  the  re- 
sultant motion  would  be  uniform  along  the  straight  line  from  A  to  E. 

Representation  of  Velocities  by  Diagrams. — Sup- 
pose that  we  wish  to  indicate  by  a  diagram  that  a  body  is 
moving  in  a  straight  line  with  a  uniform  velocity  of  15  feet 
a  second. 

Through  any  convenient  point  A  on  the  paper,  a  line  should  be 
drawn  in  any  convenient  direction  AC.     At  a  distance  of  15  units 
from  A  (fifteen  eighths  of  an  inch),  a  point  B  should  be  marked  off. 
If  a  second  motion  is  to  be  represented,  an- 
other line   A  D  should  be  drawn,  making 
the  same  angle  with  A  C  that  the  direction 
of  the  second  motion  made  with  the  first. 
Along  this  should  be  laid  off  in  the  same 
units  a  number  to  represent  the  second  veloc- 
ity;  for  instance,  if  this  is  11  feet  a  second, 
a  point  E  should  be  marked  off,  so  that  A  E 
equals  eleven  eighths  of  an  inch.     It  is  clear, 
therefore,  that  A  B  and  A  E  can  be  laid  off 
to  represent  velocities — i.  e.,  rates  of  motion  or  motions  per  units  of 
time — as  well  as  motions  merely. 
3 


FIG.  8. 


26  KINEMATICS. 

Composition  of  Uniform  Velocities. — It  has  been 
shown  how  velocities  can  be  represented  by  lines  and  dia- 
grams just  as  mere  motion  is  represented,  the  only  differ- 
ence being  that  a  unit  along  the  line  stands  for  velocity — 
i.Q.^feet  per  second  or  metres  per  second — instead  of  mere 
change  of  position — i.  e.,  feet  or  metres.  All  the  foregoing 
statements  as  to  the  composition  of  motion  apply,  therefore, 
to  the  composition  of  uniform  velocities. 

Composition  of  Uniform  Accelerations. — If  we  make 
the  direction  of  the  lines  such  as  to  represent  the  direction 
of  the  acceleration  and  the  lengths  of  the  lines  proportional 
to  the  rate  of  acceleration,  then  the  resultant  acceleration 
will  be  found  precisely  as  the  resultant  velocities  or  motions 
are  found. 

Resolution  of  Uniform  Motions.  —  Two  Compo- 
nents.— Suppose  that  a  particle  at  A  moves  uniformly  in  the 
direction  A  B,  reaching  B  in  a  certain  time ;  and  suppose, 
further,  that  we  do  not  know  anything  about  the  cause  of 
the  motion.  Then  this  motion  may  have  been  produced  by 
the  combination  of  several  motions  simultaneously  impressed 
upon  the  particle. 

Let  us  draw  any  two  straight  lines,  N  and  P,  at  random,  and  ask 
whether  motions  in  the  direction  of  these  lines  could,  if  of  the  proper 

amounts,  have  caused    the 
B  motion  over  A  B. 

Through  either  A  or  B, 
\  draw  a  line  parallel  either  to 

N  or  P,  say  A  E  parallel  to 
/  \c  P.      Through  B  draw  an- 

A/_ *p  other    line    parallel    to    N. 

These  two  lines  intersect  at 
C.     From  the   composition 
FIG.  9. -RESOLUTION.  of    motions,   page    24,    you 

know  that  a  particle  at  A, 

simultaneously  given  the  motions  A  C  and  C  B,  would  move  over  A  B. 
Hence,  you  know  that  a  motion  A  C  in  the  direction  of  P,  combined 
with  another,  C  B,  in  the  direction  of  N,  will  produce  the  given  mo- 


RESOLUTION   OF  MOTIONS.  27 

tion.    This  process  is  called  the  resolution  into  components ;  that  is. 
resolving  the  motion  into  component  motions. 

It  is  important  to  remember  that  the  motion  is  always  understood 
to  take  place  in  the  direction  indicated  by  the  order  in  which  the  let- 
ters denoting  the  line  are  written.  Thus,  motion  along  A  B  would 
mean  from  A  toward  B ;  along  B  A,  from  B  toward  A. 

Several  Components. — By  methods  based  upon  those 
for  the  composition  of  several  motions,  it  is  possible  also  to 
resolve  a  given  motion  into  any  desired  number  of  compo- 
nents in  any  desired  directions. 

A  motion  may  be  regarded  as  being  made  up  of  the 
simultaneous  motions  obtained  by  this  process  of  resolution, 
for  it  is  in  every  way  precisely  the  same  as  if  it  were  so 
made  up. 

QUESTIONS.— Draw  on  the  blackboard  a  diagram  representing  the  path  of  a  ball 
rolled  across  a  moving  car.  Explain  fully  why  the  ball  takes  such  a  course. 
What  do  you  mean  by  resultant  motion  ?  Illustrate  by  diagram.  Define  re- 
sultant velocity.  What  is  Composition  of  Motions  ?  Describe  and  apply  the 
parallelogram  of  motions.  Illustrate  in  the  case  of  a  boat  crossing  a  rapid 
stream  or  a  sail-boat  running  across  the  wind.  How  can  you  find  the  result- 
ant of  several  motions  ?  What  is  meant  by  resolution  of  motions  ?  Illustrate 
by  figure.  What  is  possible  where  there  are  several  components  ? 


MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

If  a  train  of  cars  is  moving  uniformly  at  a  rate  of  20  miles  an  hour,  how  far  will 
it  go  in  5  hours  ?  In  3  days  ?  How  long  will  it  take  the  train  to  go  1,000  miles  ? 
If  it  traveled  520  miles  in  20  hours,  moving  uniformly,  what  was  its  velocity  ? 

Wild  pigeons  have  been  shot  in  the  latitude  of  Albany,  N.  Y.,  with  Carolina  rice 
undigested  in  their  crops.  About  what  must  have  been  the  velocity  of  their 
flight  ?  (Apply  scale  to  your  map  of  the  United  States.) 

If  a  train  goes  from  Boston  to  Albany  in  6  hours  and  the  distance  is  200  miles, 
what  is  its  average  velocity  ? 

A  particle  starting  from  rest  and  given  a  uniform  acceleration  of  50  feet  a  second 
would  have  what  velocity  at  the  end  of  20  seconds  *  V  =  50  x  20.  What  dis- 
tance would  it  traverse  in  this  time  ?  Ans.  10,000  feet. 

A  particle  starting  from  rest  and  moving  with  uniformly  accelerated  motion  is 
found  to  have  a  velocity  of  100  feet  a  second  at  the  end  of  5  seconds.  What 

was  its  rate  of  acceleration  ?    a  =  ^-  =  — -   If  the  same  particle  had  been  found 

t        o. 

to  have  traveled  90  feet  in  3  seconds,  what  would  have  been  its  acceleration  ? 
a  =  -^-  What  time  would  the  particle  have  taken  to  travel  160  feet  with  this 
Acceleration  ?  Ans.  4  seconds. 


28  ENERGY. 

If  a  particle  moving  with  a  uniform  velocity  of  500  feet  a  second  were  to  be  given 
an  acceleration  of  50  feet  a  second  in  the  direction  of  its  motion,  what  would  be 
the  velocity  at  the  end  of  20  seconds  ?  v'=  500  +  (50  x  20). 

If  the  same  acceleration  were  imparted  in  the  opposite  direction,  what  would  be 
the  velocity  at  the  end  of  3  seconds  ?  v"=  500  -  (50  x  3).  What  at  the  end  of  10 
seconds  ?  v"=  500  -  (50  x  10)  =  0— i.  e.,  it  would  have  been  brought  exactly  to 
rest.  What  at  the  end  of  20  seconds  ?  v"  =500-  (50x20)=  -  500— i.e.,  the  par 
ticle  would  be  moving  in  the  opposite  direction  from  that  at  the  outset. 

What  would  be  the  distance  traversed  in  the  first  example  ?  Ans.  20,000  feet. 
What  in  the  second  ? 

Uniform  velocities  of  10  feet  per  second  northward  and  5  feet  per  second  east- 
ward are  simultaneously  given  to  a  particle.  Draw  a  diagram  by  the  parallel 
ogram  of  velocities,  which  will  show  the  relative  direction  and  magnitude  of 
the  resultant  velocity. 


ENERGY. 

NATURE  OF  ENERGY. 

Work  and  Energy  defined. — There  are  two  funda- 
mental terms — energy  and  work — which  are  used  in  physics 
in  very  nearly  the  same  sense  as  in  every-day  speech.  In 
arriving  at  their  scientific  meaning,  we  shall  begin  by  con- 
sidering the  ideas  which  they  commonly  represent  to  us. 

When  we  say  that  a  man  has  much  energy,  we  mean  that 
he  has  much  capacity  for  doing  work.  By  this  we  may  im- 
ply bodily  work  or  mental  work,  or  both ;  but  in  our  present 
study  we  are  not  concerned  with  mental  phenomena  or 
exercise  of  the  will,  so  we  need  think  only  of  the  man's 
muscular  energy  and  of  the  work  which  he  can  do  with  his 
body. 

In  physics,  when  we  say  that  an  inanimate  object  or 
portion  of  matter  has  energy,  we  mean  that  it  possesses 
capacity  to  perform  physical  work.*  Thus — 

Energy  is  capacity  for  doing  Work. 


*  Energy  is  often  spoken  of  as  the  power  of  doing  work,  or  simply  as  power 
The  term  power,  however,  has  a  special  meaning  assigned  to  it  in  physics,  and 
should  not  be  used  in  this  connection.  (See  page  101.) 


NATURE  OP  ENERGY.  29 

It  will  be  found  as  we  go  on  that  there  is  reason  to  be- 
lieve that  whenever  a  body  (that  is,  a  portion  of  matter  large 
or  small)  performs  work,  it  does  so  by  accelerating  the  mo- 
tion of  other  portions  of  matter.  In  many  cases,  this  accel- 
eration is  visible ;  in  others,  it  is  shown  only  by  close  study ; 
in  others  again,  it  is  only  supposed  (with  more  or  less  prob- 
ability) to  be  the  fact. 

By  way  of  illustration  of  the  first  class  of  cases,  find  some  heavy 
object  which  will  roll  easily — a  large  wooden  ball,  a  cannon-ball — 
anything  that  will  move  with  little  friction.  Select  a  smooth,  level 
surface  on  which  you  can  roll  it.  The  more  massive  the  object 
and  the  smoother  the  surface,  the  more  convincing  the  experiment 
will  be. 

Let  us  take  a  heavy  ball  on  a  smooth  floor.  Begin  with  the  ball  at 
rest ;  then  with  it  in  motion.  Accelerate  it  by  pushing  it.  In  order 
to  do  so,  you  will  have  to  exert  muscular  effort  in  a  manner  which  you 
will  recognize  as  what  is  familiarly  called  •"  doing  work."  Repeat  the 
experiment  in  a  variety  of  ways.  You  will  invariably  find  that  to  ac- 
celerate the  ball  you  must  perform  work  upon  it.  This  is  a  universal 
principle. 

It  is  found  also  to  be  true  that  the  amount  of  work  done  to  produce 
a  given  acceleration  in  a  given  object  is  the  same  at  whatever  velocity 
the  particle  is  already  moving ;  for  instance,  to  accelerate  its  motion 
by  10  feet  a  second  would  require  no  more  work  if  the  object  is  mov- 
ing a  mile  a  second  than  if  its  velocity  is  only  a  foot  a  second,  or  if  at 
the  outset  it  was  zero.* 

Take  another  familiar  example.  Throw  a  ball  horizontally.  All 
the  time  the  ball  is  in  your  hand  you  are  pushing  it  forward  by  the 
hand  and  continually  accelerating  it.  You  will  recognize  by  your  feel- 


*  The  student  will  find  the  whole  subject  much  clearer  and  more  interest- 
ing if  he  will  try  for  himself  the  experiments  suggested.  The  teacher  should 
see  that  this  is  done  in  every  case  where  possible,  and  should  encourage  the  pupils 
to  describe  in  the  class-room  their  own  experiments.  Learners  will  find  it  much 
easier  to  remember  the  subjects  they  study  if  they  will  talk  them  over  among 
themselves  at  unoccupied  times  out  of  school,  and  plan  to  work  together  upon 
experiments  at  home.  It  is  by  no  means  necessary  that  the  apparatus  should 
be  exactly  that  here  described.  The  spirit  and  habit  thus  acquired  of  trying 
things  for  one's  self  and  of  taking  nothing  for  granted  that  can  be  tested  by  ex- 
periment, will  be  of  untold  value  through  life  ;  while  the  ingenuity  developed  in 
constructing  apparatus,  in  using  tools,  and  especially  in  adapting  things  at  hand 
to  the  purposes  desired,  must  prove  a  most  desirable  acquisition. 


30  ENERGY. 

ing,  especially  if  you  continue  throwing  the  ball  for  a  few  minutes, 
that  you  are  doing  work  during  each  throw. 

In  each  experiment  you  should  be  able  to  discover  that  you  are  do- 
ing work  so  long  and  only  so  long  as  you  are  increasing  the  velocity  of 
the  object— i.  e.,  producing  acceleration. 

If  the  ball  had  been  set  in  motion  by  some  inanimate  material  body, 
that  body  would  have  accomplished  the  same  result  as  you.  It  would, 
therefore,  have  performed  work. 

A  body  is  performing  work  whenever,  and  as  long  as, 
it  is  causing  acceleration  of  any  other  portion  of  matter. 
When  a  body  A  is  accelerating  another  body  B,  we  say  that 
work  is  being  done  by  A  and  upon  B. 

Inertia. — As  the  result  of  all  sorts  of  experiments  upon 
all  kinds  of  material  objects,  it  appears  that  no  particle  of 
matter  of  itself  is  capable  of  changing  in  the  slightest  de- 
gree either  the  direction  or  velocity  of  its  motion.  This  is 
briefly  expressed  by  saying  that  matter  is  perfectly  inert. 
By  this  we  do  not  mean  that  a  given  particle  is  not  in  mo- 
tion, but  simply  that  it  has  no  capacity  of  itself  to  change  its 
rate  or  direction  of  motion — that  is,  if  it  is  moving  relative- 
ly to  its  surroundings  it  can  not  of  itself  change  its  direction 
or  speed,  or  if  it  is  at  rest  relatively  to  them  it  can  not  of 
itself  start  into  motion. 

From  this  statement  and  the  foregoing  experiments,  it 
follows  that  a  material  particle  can  be  accelerated  only  by 
the  performance  of  work  upon  it  by  some  other  object.  To 
be  able  to  do  work,  this  other  object  must  possess  energy. 

Whenever,  then,  a  particle  of  matter  is  being  accelerated, 
work  is  being  done  upon  it  by  some  other  portion  of  matter 
possessing  energy.*  This  fact  is  of  the  utmost  importance 
to  any  clear  comprehension  of  the  laws  of  Physics. 

*  The  above  is  not  true  in  a  general  sense  of  a  body  of  matter,  for  the  individ- 
ual particles  always  possess  some  energy  relatively  to  one  another  which  may 
act  (in  the  case  of  a  heated  body)  in  such  a  way  as  to  change  the  direction  and 
velocity  of  the  body  by  expanding  it,  or  otherwise.  The  statement  is  true,  how* 
ever,  of  any  body  as  a  whole  so  long  as  it  retains  its  size  and  form. 


NATURE  OF  ENERGY.  31 

Three  statements,  called  the  three  LAWS  OF  MOTION,  were  given  two 
centuries  ago  by  Sir  Isaac  Newton  in  his  classic  work,  the  Principia. 
They  stand  to-day  without  change  as  presenting  the  current  ideas  on 
the  same  subjects.  The  first  law,  virtually  a  statement  of  this  prop- 
erty of  matter,  is  as  follows  : 

"  Every  body  continues  in  its  state  of  rest  or  of  uniform  motion  in 
a  straight  line,  except  in  so  far  as  it  may  be  compelled  by  impressed 
forces  to  change  that  state." 

Just  what  is  meant  by  force,  you  will  learn  later.  For  the  present 
it  will  be  sufficient  if  you  understand  the  phrase  "  by  impressed  forces  " 
to  mean  by»  the  action  of  some  other  matter  possessing  energy. 

Free  Motion. — A  body  is  said  to  be  free  to  move  in  a 
given  direction  when  there  is  no  resistance  opposing  its  mo- 
tion in  that  direction.  In  its  widest  sense,  a  free  body  is 
one  whose  motion  is  unresisted  in  all  directions,  and  the 
motion  of  such  a  body  would  be  free  motion  in  the  broadest 
sense  of  the  term.  A  smooth  round  ball  rolling  on  a  truly 
horizontal  smooth  surface  is  nearly  free  to  move  in  any 
direction  over  the  surface. 

Nature  of  Energy. — A  man  is  able  to  perform  work 
because  he  possesses  muscular  energy.  We  shall  not  attempt 
to  consider  in  what  that  form  of  energy  consists,  but  we 
must  ascertain  what  is  the  condition  of  an  inanimate  object 
when  it  possesses  energy.  In  doing  so  we  shall  find  that 
matter  can  possess  energy  only  ~by  being  in  motion. 

Let  us  first  examine  the  energy  of  an  object  in  visible  motion. 
Take  two  balls,  A  and  B,  of  about  the  same  size  and  of  any  elastic  ma- 


FIG.  10.— EXPERIMENT  WITH  BALLS  ON  GROOVED  BOARD. 

terial.  Ivory  or  glass  balls  are  the  best,  but  marbles  or  croquet  or  ten- 
nis balls  will  answer.  Place  them  on  a  wide  straight  crack  in  the 
floor  or  table  or  on  a  grooved  board,  or  lay  down  a  couple  of  planed 
boards  with  edges  a  little  apart  to  serve  as  guides.  The  result  of  the 


iLAI 
v    or  THE 


.     - 

A 
iTV 


32  ENERGY. 

experiment  will  be  more  marked  if  the  end  of  the  board  toward  A  is 
raised  very  slightly,  nearly  but  not  quite  enough  to  have  the  balls  keep 
in  motion  of  themselves,  thus  overcoming  friction. 

Start  A  rolling  toward  B.  When  it  strikes,  B  will  be  accelerated — 
i.  e.,  if  at  rest  it  will  be  set  in  motion  ;  if  moving  in  the  same  direc- 
tion as  A,  it  will  be  made  to  move  faster ;  if  moving  (not  too  fast)  to- 
ward A,  it  will  be  stopped  and  set  in  motion  in  the  reverse  direction. 
All  these  are  merely  cases  of  acceleration  of  B  by  A. 

Place  A  and  B  in  contact,  but  both  at  rest.  Neither  can  accelerate 
the  other.  Let  A  and  B  roll  down  the  board  in  actual  contact,  with  the 
same  velocity.  Again,  neither  can  accelerate  the  other. 

You  see,  then,  that  A  (possessing  energy  imparted  by  you)  can  ac- 
celerate B  when  it  has  a  velocity  relatively  to  B,  and  can  not  accelerate 
B  when  it  has  no  velocity  relatively  to  it ;  but,  to  accelerate  B,  requires 
that  work  should  be  performed  upon  it.  Hence  A  must  have  possessed 
energy  relatively  to  B  when  it  had  a  velocity,  and  none  when  it  had  no 
velocity  relatively  to  B.  Again,  note  what  the  condition  of  A  is  after 
it  has  done  work  upon  B.  Its  velocity  is  much  reduced,  and  may  be 
even  zero.  A  loss  of  velocity  has  accompanied  the  performance  of 
work,  and  was  therefore  apparently  necessary  to  it. 

If  B  is  moving  toward  A  at  a  certain  speed,  A  may  not  have 
sufficient  energy  to  send  it  backward,  but  will  merely  stop  it  or  per- 
haps only  lessen  its  speed.  In  this  case  A  will  bound  back,  and  the 
work  will  therefore  have  been  done  by  B  upon  A,  as  A  will  have  been 
accelerated  while  B  will  have  lost  velocity. 

In  the  first  experiment  above,  the  acceleration  of  B  appears  to  be 
instantaneous,  but  in  reality  the  balls  are  in  contact  for  a  time  which  is 
reasonable,  although  so  short  that  we  do  not  easily  perceive  it.  During 
this  time,  the  velocity  of  A  is  diminishing  and  that  of  B  is  increas- 
ing. 

Motion  necessary  to  Energy. — From  a  multitude  of 
experiments  of  this  sort,  the  conclusion  is  drawn  that  a  body 
in  visible  motion  possesses  energy  'because  of  its  motion. 

Increase  of  Energy  with  Velocity. — Roll  A  with  dif- 
ferent velocities.  The  faster  it  moves,  the  faster  B  will 
move  after  the  blow.  To  make  B  move  faster  requires,  as 
you  know  from  your  former  experiment  in  rolling  the  ball, 
more  work  to  be  done  upon  it.  Hence  the  greater  the  ve- 
locity of  A,  the  more  work  it  can  do,  and  therefore  the  more 


NATURE   OF  ENERGY.  33 

energy  it  possesses.  The  less  the  velocity  of  A,  the  less  its 
energy.  If  its  velocity  is  zero,  its  energy  is  zero.  Therefore, 
the  energy  of  a  body  in  visible  motion  increases  with  an 
increase  of  its  velocity. 

From  general  experience  with  all  forms  of  energy,  the  hypothesis  is 
reached  that,  just  as  the  energy  which  we  have  been  dealing  with  in  the 
moving  balls  was  due  to  the  visible  motion  of  their  mass,  so  all  energy  of 
whatever  form  is  due  to  motion  of  matter.  The  motion  and  even  the 
moving  portions  of  matter  may,  however,  be  invisible,  owing  either  to 
smallness,  to  the  peculiar  character  of  the  matter,  or  to  other  causes. 

It  is  also  found,  as  will  be  shown,  that  the  amount  of  energy  depends 
on  the  amount  (mass)  of  moving  matter  as  well  as  on  its  velocity.  The 
property  of  inertia  further  indicates  to  us  that  energy  is  a  capacity  ac- 
quired by  matter  and  not  inherent  in  it.  Hence  it  is  assumed  that — 

ENERGY,  OK  THE  CAPACITY  OF  DOING  WORK,  IS  POS- 
SESSED BY  MATTER  I^  VIRTUE  OF  ITS  MASS  AND  VELOCITY. 

When  we  speak  of  a  body,  then,  as  possessing  energy,  we  mean  that 
the  matter  of  the  body  is  in  motion,  either  visible  or  invisible.  In 
other  words,  we  mean  that  the  body  itself  contains  the  energy.  In 
contrast  to  this  you  will  see,  as  you  go  on,  abundant  instances  where 
bodies  are  performing  work  (as  where  a  weight  runs  a  clock),  but  where 
the  energy  is  not  possessed  by  the  body  but  only  transmitted  through 
it.  In  such  a  case  the  energy  is  imparted  to  the  body  by  the  source  of 
energy,  and  given  up  by  the  body  to  the  thing  worked  upon. 

Inasmuch  as  it  is  often  convenient  to  use  a  term  which 
suggests  the  idea  of  motion  when  energy  is  referred  to,  the 
adjective  kinet'ic  is  sometimes  prefixed  to  the  word. 

QUESTIONS.— What  do  we  mean  when  we  say  a  man  possesses  energy  ?  Give  the 
ordinary  meaning  of  the  term  energy  ;  the  definition  of  energy  as  used  in  phys- 
ical science.  What  do  we  mean  in  physics  by  the  term  body  ?  What  is  be- 
lieved always  to  occur  when  work  is  done  ?  Is  this  known  always  to  occur  ? 
Why  not  ?  If  you  accelerate  a  rolling  ball  by  pushing  it  with  your  hand,  how 
do  you  recognize  that  you  are  doing  work  ?  Can  matter  be  accelerated  in  any 
way  except  by  doing  work  upon  it  ?  If  a  ball  is  at  rest  upon  the  floor  and  you 
set  it  in  motion  so  that  its  velocity  is  one  foot  a  second,  is  the  work  done  by  you 
any  greater  or  any  less  than  if  the  ball  had  been  moving  with  a  velocity  of  5 
feet  a  second  and  you  had  increased  it  to  6  feet  ?  How  would  you  explain  this 
from  the  statements  concerning  rest  as  given  under  Kinematics  ?  If  the  ball  ia 
rolling  without  friction  at  a  uniform  speed,  do  you  have  to  do  work  to  keep 
up  that  speed  ? 


34  ENERGY. 

When  do  we  say  that  an  inanimate  body  is  performing  work  ?  When  do  we  say 
that  a  body  is  having  work  done  upon  it  ?  Is  any  particle  of  matter  capable  of 
starting  itself  into  motion  ?  Of  stopping  itself  ?  Of  changing  its  velocity  in 
any  way  ?  Of  changing  the  direction  of  its  motion  ?  Of  accelerating  or  re- 
tarding itself  ?  What  term  do  we  use  to  express  the  inability  of  matter  to  do 
these  things  ?  Does  Inertia  mean  anything  else  ?  Suppose  a  bullet  is  moving 
2,000  feet  a  second,  is  it  inert  ?  Suppose  that  the  same  bullet  is  lying  motion- 
less on  the  floor,  is  it  any  more  or  less  inert  than  when  moving  ?  By  declaring 
a  body  to  be  inert,  do  we  thereby  declare  anything  respecting  its  motion  ? 

State  Newton's  first  law  of  motion.  What  is  meant  by  free  motion  ?  By  a  free 
body  ?  How  is  it  found  that  matter  can  possess  energy  ?  Can  it  possess  energy 
in  any  other  way  ?  What  does  the  experiment  with  the  rolling  balls  show  as  to 
the  velocity  of  A  with  respect  to  B  in  order  that  A  should  be  capable  of  doing 
work  upon  B  ?  How  does  this  illustrate  that  a  body  in  visible  motion  possesses 
energy  ?  How  that  it  possesses  energy  because  of  its  velocity  ?  If  the  velocity 
is  greater,  is  the  energy  greater  or  less  ?  Prove  this  by  experiment.  Give  the 
fundamental  general  hypothesis  respecting  the  nature  of  energy.  Is  this  based 
on  experimental  knowledge,  or  is  it  purely  a  matter  of  belief  ?  What  do  we 
mean  by  saying  that  a  body  "  possesses  "  energy  ?  Is  the  motion  to  which  en- 
ergy is  due  always  visible  ?  Is  energy  due  to  anything  except  velocity  ?  Is 
energy  the  same  as  velocity  ?  Could  an  imaginary  moving  point  possess  en- 
ergy ?  Can  a  body  transmit  energy  which  it  does  not  possess  ?  Give  an  illus- 
tration. What  is  meant  by  kinetic  energy  ?  What  is  the  meaning  of  the  adjec- 
tive kinetic  ?  Is  all  energy  kinetic  ? 


FORMS  OF  ENERGY. 

The  Kind  of  Motion,  in  virtue  of  which  a  body  pos- 
sesses energy,  makes  a  difference  in  the  sensations  which 
that  energy  excites  in  us,  as  well  as  a  difference  in  the  effects 
which  it  produces  when  doing  work  upon  other  bodies.  For 
this  reason,  energy  is  said  to  exist  in  various  forms. 

Examples  of  Forms  of  Energy. — Of  the  different 
kinds  of  motion,  there  is,  first,  visible  motion  of  the  body  as 
a  whole,  moving  along  through  space ;  this  gives  rise  to  en- 
ergy of  visible  onward  motion.  A  body  may  rotate  or  spin 
like  a  wheel  or  top,  and  its  energy  is  then  in  the  form  of 
visible  energy  of  rotation.  It  may  not  be  in  visible  motion 
at  all,  but  possess  only  invisible  motion  of  its  particles  or 
molecules ;  its  energy  is  then  in  the  form  which  is  called 
heat,  sound,  radiant  energy,  according  to  the  precise  charac- 
ter of  the  molecular  motion.  Finally,  energy  may  be  in  the 
form  exhibited  by  electrical  currents,  etc. 


FORMS  OF  ENERGY.  35 

These  varied  forms  will  be  considered  in  detail  in  the 
chapters  on  Sound,  Heat,  Light,  Electricity,  and  Magnet- 
ism. A  few  examples,  however,  will  be  here  given  in  some 
detail,  as  it  is  of  the  utmost  importance  to  any  real  knowl- 
edge of  physics  to  obtain  clear  ideas  of  energy. 

Energy  of  Visible  Onward  Motion. — To  prove  that  a 
body  possesses  energy  (actual,  kinetic)  with  reference  to  a 
given  point,  we  have  only  to  show  that  its  velocity  with  ref- 
erence to  this  point  is  greater  than  zero.  As  motion  is 
purely  relative,  we  must  remember  that  the  velocity,  and 
therefore  the  energy,  will  be  different  in  amount  according 
to  the  point  to  which  they  are  referred,  for  the  velocity  re- 
ferred to  one  point  may  be  large,  to  another  small. 

Two  cannon-balls  fired  at  the  same  instant,  in  the  same  direction 
and  with  the  same  velocity,  would  have  immense  energy  referred  to 
the  cannon  they  had  left,  or  to  the  ground  they  were  moving  over, 
or  to  the  target  at  which  they  were  aimed.  But  relatively  to  each 
other  they  would  possess  no  energy  at  all,  because  their  relative  ve- 
locity is  zero,  just  as  two  parts  of  the  same  ball  would  have  no  energy 
with  reference  to  each  other. 

A  railroad  train  in  motion  over  the  track  possesses  energy  with 
respect  to  any  object  stationary  upon  the  track,  or  moving  more  slowly 
than  itself.  Witness  the  destruction  produced  if  the  train  runs  into 
another  which  is  standing  still,  or  even  moving  slowly  ahead  of  it.  If 
another  train  be  approaching  the  first,  then  the  velocity  of  the  two 
trains  relatively  to  each  other  is,  of  course,  the  sum  of  their  separate 
velocities  relative  to  the  track.  Their  energy  relative  to  each  other  is 
therefore  much  greater  than  their  energy  relative  to  a  stationary  train ; 
while  if  there  are  two  trains  moving  in  the  same  direction  with  the 
same  velocity,  they  possess  no  energy  relatively  to  each  other,  although 
both  have  great  energy  relative  to  the  track  and  earth. 

A  stone  lying  upon  the  ground  possesses  no  energy  relative  to  the 
ground,  but  think  of  the  velocity  with  which  the  stone  is  moving,  to- 
gether with  the  ground  beneath  it,  as  the  earth  spins  on  its  axis  once 
each  day,  and  whirls  along  on  its  path  around  the  sun ;  and  imagine 
the  immense  energy  it  possesses  relative  to  a  point  not  so  moving. 

Energry  of  Visible  Vibration. — Suspend  a  stone  or 
any  heavy  object  by  a  string.  The  stone  will  hang  straight 


36  ENERGY. 

downward.  Pull  it  aside  a  few  inches  in  a  horizontal  direc- 
tion, and  let  it  go.  It  will  swing  to  and  fro.  Notice  that, 
when  you  release  it,  it  begins  to  move  slowly  at  first,  then 
more  and  more  rapidly,  till  it  reaches  the  lowest  point  of  its 
swing,  and  then  it  moves  more  and  more  slowly  as  it  rises  to 
the  other  end  of  the  sweep.  There  it  stops  and  then  begins 
its  return  swing.  Notice  also  that  it  always  takes,  as  nearly 
as  you  can  tell,  just  the  same  time  for  each  swing  made.  A 
body  suspended  and  swinging  in  this  way  is  called  a  pendu- 
lum, and  the  to-and-fro  motion  of  the  stone  or  "  bob  of  the 
pendulum  "  is  pendular  motion,  or  vibration. 

Examine  now  the  energy  of  the  stone.  You  will  see  that  the  in- 
stant you  release  it,  arid  before  it  starts,  it  has  no  velocity,  and  there- 
fore no  energy.  As  it  moves  it  gradually  gains  energy,  for  its  motion 
is  accelerated  until  it  reaches  the  lowest  point.  Then  it  begins  to  lose 
velocity,  and  therefore  energy,  moving  with  retarded  motion,  and  so 
continues  until  it  reaches  its  turning-point,  where  for  an  instant  its 
velocity  is  zero,  and  it  therefore  possesses  no  energy.  The  same  series 
of  changes  is  gone  through  with  at  each  swing.  The  energy  of  a  body 
vibrating  in  this  way  is  called  energy  of  vibration,  or  vibratory  energy. 
Place  a  rubber  band  over  the  tips  of  your  thumb  and  forefinger, 
and  keep  it  stretched  by  drawing  them  apart.  With  the  other  hand 

pluck  the  band  near  the  middle. 
This  will  set  it  in  vibration,  and  it 
will  give  out  a  musical  note.  The 
string  of  any  musical  instrument  will 
show  the  same  thing.  Examine  the 
vibrating  side,  and  you  will  see  that 
it  is  in  to-and-fro  motion.  Touch  a 
bit  of  paper  against  it,  and  a  buzzing 
FIG.  11.— VIBRATING  BAND.  sound  will  be  heard  as  the  band  re- 

peatedly strikes  the  paper.  Each  par- 
ticle of  the  band  is  moving  with  a  motion  very  similar  in  character  to 
that  of  the  pendulum.  Now,  the  band  is  a  material  substance,  and  you 
have  found  that  it  is  in  motion.  It  therefore  possesses  energy.  We 
refer  the  motion  and  energy  to  the  position  of  the  band  when  at 
rest. 

Sound   Vibration. — When   the   band   is   vibrating,   a 
sound  is  heard.     This  sound  comes  to  your  ears  through  the 


FORMS  OP  ENERGY.  tf 

air.  The  vibrating  string  imparts  its  energy  to  the  air,  set- 
ting the  air  particles  into  a  similar  to-and-fro  (pendular) 
vibration.  Pulsations  are  thus  begun  in  the  air  which  travel 
off  from  the  band  in  all  directions,  much  as  waves  of  water 
travel  when  a  pebble  is  dropped  into  a  pool.  Some  of  these 
pulsations  reach  the  ear  and  cause  there  the  sensation  of 
sound.  The  particles  of  air  are  matter.  They  are  in  to- 
and-fro  motion  when  conveying  sound.  They  therefore  pos- 
sess energy  just  as  does  the  vibrating  string  itself,  and  this 
energy  we  call  the  energy  of  sound  vibrations. 

Sound  vibration  is  thus  energy  of  motion,  but  the  motion,  unlike 
that  of  the  pendulum,  for  instance,  is  invisible,  and  it  excites  in  us  a 
sensation  (sound)  which  the  pendulum  does  not.  It  is  therefore  called 
another  form  of  energy. 

Heat. — In  a  body  conveying  or  giving  out  sound,  the 
molecules  are  vibrating  in  a  very  regular  and  systematic 
manner,  all  the  molecules  at  any  given  point  of  the  body 
swinging  to  and  fro  together  in  nearly  the  same  direction 
and  at  nearly  the  same  rate.  The  regularity  may  be  com- 
pared to  that  of  the  steps  of  a  body  of  soldiers  marching  in 
correct  time. 

But  the  molecules  of  all  bodies  possess,  whether  in  sound 
vibration  or  not,  another  and  entirely  distinct  motion.  They 
are  never  without  some  of  this  motion ;  no  body  has  been 
ever  known  to  be  reduced  to  a  condition  where  it  was  ab- 
sent. This  motion  differs  from  that  of  sound  vibration  in 
being  irregular  and  unsystematic,  when  we  consider  the 
movement  of  the  individual  particles.  The  molecules  are 
flying  to  and  fro,  first  in  one  direction,  then  in  another,  no 
two  at  once  in  the  same  direction,  now  fast,  now  slowly,  jos- 
tling against  their  neighbors  and  being  jostled  in  turn.  The 
irregularity  of  this  motion  may  be  compared  to  that  of  the 
footsteps  of  the  individuals  in  a  great  crowd  of  people,  no 
two  of  whom  are  trying  to  move  in  the  same  direction  or  at 
the  same  rate  of  speed.  Each  molecule  at  any  given  instant 


38  ENERGY. 

has  a  definite  velocity  (relative  to  a  fixed  point  upon  the 
body  or  vessel  holding  it),  and  in  virtue  of  its  mass  and  this 
velocity  it  possesses  energy. 

Such  energy  is  Heat.  The  more  violently  the  particles 
are  flying  about,  the  hotter  is  the  body.  Now,  you  easily 
perceive  that  heat  affects  our  senses  in  a  manner  entirely 
different  from  sound,  or  from  the  energy  of  an  onward  mov- 
ing body.  Hence,  heat  is  another  form  of  energy. 

Radiant  Energy. — Light. — We  have  reason  to  believe 
that  all  bodies  are  surrounded  by  a  kind  of  matter  which 
possesses  many  properties  quite  different  from  those  charac- 
terizing substances  with  which  we  are  familiar.  This  mat- 
ter is  called  the  luminiferous  Ether,  or  simply  the  Ether. 
You  will  learn  more  about  it  when  you  come  to  study  Light. 

The  molecules  of  bodies,  as  they  leap  about  in  performing 
the  heat  movements,  stir  up  this  ether  at  the  points  where 
it  is  in  contact  with  them,  and  set  its  particles  into  pendu- 
lar  vibration.  This  motion  is  passed  along  in  a  wave  in  all 
directions  from  the  hot  body.  Each  particle  of  the  ether 
must  be  supposed  to  possess  mass,  and,  as  it  has  also  this 
motion,  it  must  possess  energy.  Such  energy  is  called  Ra- 
diant Energy. 

If  radiant  energy  falls  upon  the  skin,  it  may  excite  the  sensation  of 
warmth.  If  it  is  of  the  right  rate  of  vibration,  and  falls  upon  the  eye, 
it  excites  the  sensation  of  light.  It  is  by  means  of  radiant  energy  that 
we  are  able  to  see.  If  it  falls  upon  certain  prepared  "  plates,"  it  pro- 
duces chemical  effects  which  we  make  use  of  in  taking  photographs. 
It  also  stimulates  the  growth  of  plants ;  and,  curiously  enough,  it 
has  been  recently  proved  that  certain  electrical  effects  are  propagated 
through  space  by  this  same  radiant  energy. 

Notice  that  of  this  form  of  energy  we  know  hardly  anything  by 
direct  observation.  We  are  acquainted  with  its  effects  and  its  laws ; 
but  we  do  not  even  know  that  there  is  an  ether  in  the  same  sense  in 
which  we  know  that  air  exists.  We  feel  sure  that  there  must  be  an 
ether,  that  it  must  be  material,  and  that  it  must  transmit  energy,  be- 
cause we  have  various  effects  which  we  can  explain  by  these  supposi- 
tions without  violating  any  of  the  better  known  laws  of  matter. 


CONSERVATION  OF  ENERGY.  39 

QUESTIONS.— What  is  meant  by  the  term  "  form  of  energy  "  ?  What  would  be  the 
form  of  energy  possessed  by  a  moving  cannon-ball  ?  By  an  avalanche  ?  By  an 
arrow  in  its  flight  ?  By  the  earth  in  its  motion  through  space  ?  By  the  earth 
in  virtue  of  its  rotation  about  its  axis  ?  Give  other  examples  of  this  form.  Do 
the  cars  of  a  train  possess  any  energy  of  onward  motion  with  reference  to  one 
another  when  moving  steadily  ?  If  the  forward  car  is  suddenly  checked  by 
brakes,  a  collision,  or  by  running  off  the  track,  do  the  cars  behind  possess 
any  energy  relatively  to  it  ?  Two  trains  are  moving  with  the  same  speed  on 
the  same  track  ;  if  in  the  same  direction,  do  they  possess  energy  relatively  to 
each  other  ?  If  in  opposite  directions  ? 

Show  how  the  swinging  pendulum  possesses  energy  ?  What  is  this  form  called  ? 
At  the  extreme  end  of  its  swing,  does  the  pendulum  possess  energy  ?  What  is 
supposed,  then,  to  have  become  of  the  energy  which  is  possessed  by  the  mov- 
ing pendulum  ?  What  is  the  kind  of  motion  of  a  violin-string  when  giving 
out  sound  ?  What  is  the  energy  of  this  form  called  ?  Why  do  we  call  this  a 
different  form  of  energy  ?  To  what  do  we  refer  the  energy  and  motion  of  a 
vibrating  body  ? 

How  does  the  energy  of  sound  vibration  differ  from  that  of  the  pendulum  ?  De- 
scribe briefly  this  form  of  energy.  Describe  briefly  the  motion  constituting 
heat-energy.  That  constituting  radiant  energy.  What  proof  have  we  of  the 
existence  of  an  ether  ? 


TRANSFORMATION  AND  CONSERVATION  OF  ENERGY. 

Energy  indestructible. — When  the  properties  of  mat- 
ter are  considered,  it  will  be  shown  that  matter  is  inde- 
structible, or,  in  other  words,  that  the  quantity  of  matter  in 
the  universe  appears  to  be  constant.  The  same  statement  is 
true  of  energy,  but  of  no  other  physical  quantity.  We  have 
seen  that  energy  may  exist  in  several  forms.  It  is  also  true 
that  energy  of  any  one  form  may  be  changed  into  energy  of 
any  other  form,  or,  as  we  say,  may  be  transformed.  But, 
although  it  may  be  changed  in  form  as  much  and  as  often 
as  we  please,  and  although  such  changes  are  going  on  with- 
out ceasing  all  around  us,  yet  no  portion  of  energy  is  ever 
lost  or  destroyed. 

Whenever  a  given  quantity  of  energy  disappears  at  any 
place,  an  exactly  equivalent  amount  appears  somewhere  at 
the  same  instant,  either  in  the  same  or  different  forms. 
Thus,  the  total  quantity  of  energy  in  the  universe  appears 
to  be  constant.  This  law  is  known  as  the  principle  of 
Conservation  of  Energy. 


40  ENERGY. 

We  must  remember,  then,  that  nothing  but  energy  can  be  the  cause 
of  energy ;  and  that,  if  energy  disappears  in  a  given  place,  an  equiva- 
lent amount  must  somewhere  be  produced.  We  can  change  the  place 
or  form  of  energy,  but  we  can  neither  create  nor  destroy  it  any  more 
than  we  can  create  or  destroy  matter. 

In  familiar  language  we  speak  of  energy  as  appearing  or  disappear- 
ing; as  being  generated,  consumed,  lost,  etc.  But  this  is  allowable 
solely  as  a  matter  of  convenience. 

The  Law  of  Conservation  of  Energy  is  wholly  based 
upon  experiment  and  measurement,  as  are  all  physical  laws. 
We  know  of  no  exception  to  it.  The  confidence  which 
physicists  have  in  it  is  so  great  that  it  is  used  as  a  test  to 
determine  whether  anything  is  or  is  not  energy.  If  the 
thing  in  question  can  be  changed  into  one  or  more  known 
kinds  of  energy,  or  if  any  known  kind  of  energy  can  be 
transformed  into  it,  then  it  is  believed  to  be  energy. 

Instances  of  Transformation  of  Energy  and  examples 
of  various  forms  will  now  be  given.  Many  more  will  come 
up  incidentally  as  we  go  on.  It  is  not  possible  at  this  stage 
of  advancement  for  the  pupil  to  measure  the  quantities  of 
energy  transformed ;  the  mere  fact  of  transformation  alone 
will  be  shown : 

Eub  the  fingers  briskly  to  and  fro  upon  any  surface,  say  of  cloth 
or  wood,  and  you  will  feel  a  sensation  of  warmth,  due,  of  course,  to 
heat.  You  have  expended  muscular  energy  in  moving  the  hand  back- 
ward and  forward  against  the  resistance  of  friction,  and  heat  has 
been  produced.  The  more  the  muscular  energy  expended,  the  greater 
the  amount  of  heat  generated.  The  muscular  energy  is  changed  into 
the  form  of  energy  which  we  call  heat  (page  37). 

Rub  briskly  over  a  cloth  or  wooden  surface  a  smooth  light  piece  of 
metal,  such  as  a  button  or  a  thin  key.  It  will  soon  become  warm,  and 
even  quite  hot  to  the  touch.  Here,  again,  muscular  energy  has  been 
transformed  into  heat  energy. 

Place  a  lump  of  lead  upon  an  anvil.  Strike  it  a  blow  with  a  heavy 
hammer.  The  lump  will  be  crushed  out  of  shape,  and  you  will  find, 
on  picking  it  up,  that  it  is  quite  warm.  At  the  instant  before  striking, 
the  hammer,  owing  to  its  mass  and  velocity,  possessed  energy  of  on- 
ward motion  imparted  by  the  person  and  by  gravity.  On  striking  the 


AVAILABILITY  OF  ENERGY.  41 

lead  the  hammer  is  brought  nearly  to  rest,  and  therefore  loses  nearly 
all  this  energy.  The  equivalent  of  most  of  this  energy  appears  in  the 
form  of  heat  in  the  lead.  Here,  then,  energy  of  onward  motion  is  con- 
verted into  heat.  Not  all  the  energy  is  thus  transformed,  however, 
for  part  remains  in  the  rebounding  hammer,  and  part  is  transferred  to 
the  anvil,  setting  it  into  slight  motion.  The  hammer  and  the  anvil  are 
also  set  into  sound  vibration,  some  of  the  energy  being  thus  changed 
into  that  form  of  energy. 

Availability  of  Energy. — When  energy  is  transformed, 
it  usually  happens  that  not  all  the  energy  of  the  given  form 
can  be  changed  into  the  desired  form,  but  that  some  part 
(usually  a  considerable  part)  is  incidentally  and  unavoidably 
changed  into  other  forms  which  are  not  desired  and  are  of 
no  use  to  us.  This  follows  from  certain  laws  of  energy 
which  can  not  be  here  considered,  and  which  lead  us  to 
regard  some  forms  of  energy  as  of  a  higher  grade  than 
others. 

The  quantity  of  energy  thus  changed  into  forms  not  de- 
sired and  not  available  for  our  purposes  at  the  time,  is  often 
spoken  of  as  wasted  or  lost ;  but  you  will  see  that  it  is  still 
energy,  and  is  only  wasted  or  lost  in  the  sense  of  not  being 
available  for  the  purpose  in  hand. 

Examples  of  unavailable  heat  resulting  from  the  expenditure  of 
energy  by  man  or  by  machines  are  of  every-day  occurrence  and  often 
occasion  great  inconvenience. 

A  saw  used  to  cut  wood  or  metal  becomes  warm  or  even  hot ;  a  drill 
or  gimlet  is  heated  as  the  hole  is  bored  ;  a  file  "  heats  "  when  in  opera- 
tion on  a  piece  of  metal ;  a  car-wheel  grows  hot  when  the  brakes  are 
applied.  The  saw  and  drill  are  sometimes  oiled  in  order  to  reduce  the 
friction  and  thus  lessen  the  work  done  in  turning  them ;  the  heat  pro- 
duced is,  of  course,  diminished  in  the  same  proportion.  A  shaft, 
journal,  or  axle  of  any  kind,  if  not  properly  oiled  to  reduce  friction, 
would  heat  very  much  in  its  bearings,  causing  the  destruction  or  injury 
of  the  bearing,  or  at  least  making  it  impossible  to  turn  the  shaft.  In- 
stances of  this  are  to  be  seen  in  a  "  set "  wagon-wheel  and  the  "  hot 
box"  on  the  railroad  train. 

In  all  these  cases  the  heat  is  a  serious  cause  of  inconvenience.    It  is 
here  a  kind  of  energy  which  is  not  wanted,  and  its  production  causes 
a  waste  of  the  energy  of  the  operator  or  the  machinery. 
4 


42  ENERGY. 

Potential  Energy. — Bodies  are  frequently  so  situated 
with  respect  to  some  kind  of  energy — for  example,  that 
causing  gravitation  or  electrical  and  magnetic  effects — that 
if  left  free  to  move  they  will  themselves  acquire  energy.  In 
such  instances,  the  body  does  not  possess  actual  energy,  but 
only  the  possibility  of  acquiring  it.  It  is  said  to  possess 
potential  or  possible  energy. 

Thus  any  object  anywhere  above  the  earth's  surface,  whether  mov- 
ing in  any  direction  or  at  rest,  is  said  to  possess  potential  energy  with 
reference  to  the  surface.  This,  however,  is  not  energy  actually  pos- 
sessed by  the  object,  but  is  merely  a  convenient  phrase  to  denote  the 
energy  which  the  object  can  acquire  by  moving  from  its  given  position 
to  the  surface  of  the  earth. 

A  piece  of  iron  at  a  distance  from  a  magnet  possesses  potential  en- 
ergy with  reference  to  the  magnet,  because,  if  allowed  to  move,  it  will 
acquire  actual  energy  in  moving  toward  the  magnet. 

Work  further  defined. — In  all  these  illustrations  of 
the  change  of  place  or  form  of  energy,  the  process  of  trans- 
ference or  of  transformation  is  called  Work.  Thus,  when 
A  accelerates  B  (page  31),  we  say  that  A  does  work  on  B. 
When  we  rub  the  metal  and  produce  heat  (page  40),  we  do 
work ;  when  the  hammer  strikes  the  piece  of  lead  (page  40), 
it  performs  work  upon  the  lead.  Every  such  case  has  been 
shown  to  be  merely  a  change  in  place  or  form  of  energy. 
We  may  therefore  conclude  that 

Work  is  merely  the  process  of  changing  the  place 
or  form  of  energy. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

What  have  you  learned  in  regard  to  the  indestructibility  of  matter  ?  Explain 
fully  what  is  meant  by  the  transformation  and  conservation  of  energy.  If  en- 
ergy disappears,  what  are  we  to  infer  ?  Are  there  exceptions  to  the  Law  of 
Conservation  of  Energy  ?  Give  instances  of  the  transformation  of  energy,  re- 
peating  those  explained  in  the  book,  and  drawing  upon  your  own  experience. 

Show  by  illustrations  that  energy  when  transformed  is  not  all  available. 

Explain  and  illustrate  potential  energy. 

When  the  clapper  strikes  the  bell,  into  what  is  its  energy  of  onward  motion 
transformed  ? 


NATURE  AND  ACTION   OF  FOBCE.  4.3 

When  a  hot  body  is  giving  rise  to  vibrations  in  the  ether,  into  what  kind  of  energy 
is  its  heat-energy  transformed  ? 

The  steam-engine  transforms  what  kind  of  energy  into  the  energy  of  onward  mo- 
tion of  the  train  ? 

A  cannon  ball,  striking  a  target,  becomes  heated.  Suppose  all  its  energy  of  on- 
ward motion  were  converted  intc  heat-energy,  what  would  be  the  result  ? 

A  bullet  or  cannon-ball  striking  a  target  or  armor  becomes  heated.  A  large  part 
of  its  energy  is  converted  into  heat-energy  hi  itself  and  in  the  object  pene- 
trated and  crushed.  Suppose  all  its  energy  were  to  be  converted  into  heat  at 
the  blow,  how  hot  would  the  ball  be  ? 

Meteorites,  or  shooting-stars,  are  masses  of  material  which  enter  our  atmosphere 
from  space  and  fall  by  their  weight  toward  the  earth  They  enter  with,  or 
acquire,  a  very  great  velocity  While  moving  through  the  air  with  this  speed, 
they  experience  resistance,  in  overcoming  which,  heat  is  produced  in  sufficient 
amount  to  raise  them  to  the  red  or  white  heat  that  renders  them  visible.  What 
kinds  of  energy  are  here  transformed,  and  how  ? 

Explain  the  meaning  of  the  terms  uniform  motion,  uniformly  accelerated  mo 
tion,  retarded  motion,  and  state  again  how  such  effects  are  produced. 

If  while  a  steam-launch  is  in  motion  the  smoke  rises  vertically,  what  must  be  the 
direction  of  the  wind  ?  What,  its  velocity  ? 

Imagine  yourself  on  an  observation-car  traveling  at  a  high  rate  of  speed.  If  you 
should  throw  a  ball  vertically  upward,  what  would  be  the  appearance  of  its 
path  to  an  observer  not  on  the  train  ?  Draw  a  diagram  showing  its  actual 
path. 

Account  for  the  fact  that  it  is  as  easy  to  pitch  quoits  on  the  deck  of  a  rapidly 
moving  ocean  steamer  as  on  land. 


FORCE. 

NATURE  AND  ACTION  OF  FORCE.— WEIGHT. 

Tendency  to  Acceleration.— When  the  ball  A  of  ex- 
periment on  page  31  strikes  B  and  accelerates  it,  the  action 
is  not  instantaneous,  but  merely  of  very  brief  duration. 
Time  is  required  to  accelerate  any  mass  of  matter,  however 
small.  During  this  time  of  action,  the  velocity  of  B  is 
gradually  increased  by  the  action  of  the  energy  of  A ;  and 
we  may  say  that,  while  the  action  is  going  on,  B  has  a  ten- 
dency to  acceleration  with  respect  to  A.  By  this  we  mean 
that  B  will  be  accelerated,  unless  some  resistance  is  offered. 

In  genera!  then,  if  a  body  is  said  to  have  a  tendency  to 
acceleration,  we  imply  that  Its  motion  will  be  accelerated 


44  FORCE. 

unless  some  resistance  acts  to  prevent.  It  mil  therefore 
be  understood  that  the  tendency  is  spoken  of  as  existing, 
whether  the  acceleration  occurs  or  not. 

It  is  clear  in  this  case  that  the  tendency  to  acceleration 
is  due  to  the  action  of  the  energy  of  A  upon  B.  As  there  is 
reason  to  believe  that  acceleration  can  never  be  produced  by 
anything  but  energy,  so  tendency  to  acceleration  must  al- 
ways be  due  to  the  action  of  energy. 

In  this  experiment  the  duration  of  the  contact  between  A  and  B, 
and  therefore  of  the  tendency  to  acceleration,  was  very  brief.  But  we 
have  many  examples  of  continuous  tendencies.  For  instance,  any  ob- 
ject tends  to  fall  (with  acceleration)  toward  the  earth.  This  tendency 
is  continuous.  A  piece  of  iron  near  a  magnet  tends  continuously  to 
approach  the  magnet. 

Force. — This  action  by  which  some  forms  of  energy 
sometimes  produce  in  bodies  a  tendency  to  acceleration  is 
called  Force.  We  may  then  define  force  as  being  that  action 
of  energy  by  which  it  produces  a  tendency  to  acceleration. 
It  is  therefore  merely  an  action  of  energy  upon  bodies. 

FAMILIAR  EXAMPLES  OF  TENDENCY  TO  ACCELERATION,  OR  FORCE. — 
Hold  this  book,  or  any  object,  in  your  hand,  just  above  the  table. 
Let  go  your  hold.  It  falls  downward  until  it  reaches  the  table,  or 
some  other  object  which  interrupts  its  motion.  Here,  then,  is  a 
tendency  to  acceleration  —  and  thus,  a  force.  This  force  we  call 
Weight. 

Tear  off  some  bits  of  newspaper  not  larger  than  the  letters  of  this 
book.  Take  your  eraser,  or,  better,  a  piece  of  vulcanite,  such  as  a  hard 
rubber  comb,  or  a  fountain  or  stylographic  pen.  Rub  it  once  slowly 
over  your  hand.  Bring  it  just  over  the  bits  of  paper.  They  do  not 
move.  Wipe  the  vulcanite  dry,  then  rub  it  briskly  for  a  few  seconds 
upon  any  dry  woolen,  silk,  or  fur,  and  immediately  bring  it  again  over 
the  bits.  They  fly  up,  and  perhaps  stick  to  it.  Here  is  tendency  to 
motion,  or  force,  due  to  another  cause,  Electrification. 

In  many  instances  a  sensation  of  push  or  pull  enables  us  to  recog- 
nize the  presence  of  a  force,  as  when  we  are  holding  an  object  in  the 
hand.  It  may  aid  us  if  we  think  of  force  as  a  push  or  pull  (due  to 
energy  of  some  kind),  but  we  must  not  regard  this  as  a  definition  of 
force. 


NATURE  AND  ACTION  OP  FORCE.  45 

Action  of  Force. — In  speaking  of  acceleration  or  other 
effects,  such  as  compression,  bending,  stretch,  etc.,  we  should 
speak  of  them  as  due  to  the  action  of  energy,  for  only 
energy  can  produce  them.  But  it  is  often  more  convenient 
to  speak  of  them  as  due  to  the  action  of  the  force  instead 
of  to  that  of  the  energy  which  causes  the  force.  A  force, 
it  will  be  seen,  can  have  no  capacity  to  do  work;  such 
capacity  is  energy.  It  is  of  very  great  importance  that  this 
fact  should  be  borne  in  mind  whenever  work  or  anything 
else  is  spoken  of  as  due  to  the  action  of  force. 

Line  of  Action  of  a  Force. — The  direction  in  which 
the  body  tends  to  be  accelerated  is  called  the  direction  of 
the  force.  The  particular  line  along  which  a  particle  or 
body  tends  to  be  accelerated  is  called  the  line  of  action  of 
the  force. 

Two  or  more  Particles  necessary  to  a  Force. — We 

shall  find,  as  we  go  on,  that  whenever  any  body  or  particle 
has  a  tendency  to  acceleration,  we  have  reason  to  believe  that 
there  is  somewhere  another  body  or  particle  which  tends  to 
be  accelerated  toward  or  away  from  the  first  at  the  same 
time.  The  tendency  to  acceleration  never  belongs  to  a  sin- 
gle body  only,  or  to  a  single  particle  of  matter,  but  is  always 
a  tendency  of  two  or  more  bodies  or  particles  to  approach,  or 
recede  from,  one  another  with  an  accelerated  motion.  For 
example,  during  the  time  that  the  balls  A  and  B  are  in 
contact,  each  is  pushing  the  other.  Objects  tend  to  fall 
toward  the  earth,  but  the  earth  at  the  same  time  tends  to 
fall  toward  the  objects.  The  paper  bits  and  the  rubbed 
body  tend  to  approach  each  other. 

Recognition  of  the  Presence  of  a  Force. — We  have 
just  shown  that  a  tendency  to  acceleration  may  exist  when 
there  is  no  acceleration,  as  well  as  when  there  is.  It  is  es- 
sential that  we  should  know  how  to  recognize  the  presence 
of  a  force  in  all  cases.  There  are  two  methods : 


46  FORCE. 

1.  By  the  acceleration  produced. 

2.  By  showing  that  there  is  a  counterbalancing  force. 

The  first  method  detects  and  studies  any  unbalanced  force — i.  e., 
one  acting  on  a  body  free  to  move.  The  second  detects  as  far  as  pos- 
sible any  balanced  force — i.  e.,  one  acting  where  the  body  is  not  entirely 
free  to  move.  As  balanced  and  unbalanced  forces  often  exist  together, 
both  methods  must  be  applied  in  all  cases. 

Force  recognized  by  Acceleration. — If  a  free  body  is 
acted  upon  by  force,  its  motion  will  be  accelerated  or  re- 
tarded as  long  as  the  force  continues.  Hence,  if  a  free  body 
shows  acceleration,  we  know  that  a  force  must  be  present 
(that  is,  that  energy  must  be  acting  on  the  body) ;  and  so 
long  as  the  acceleration  continues,  we  know  that  the  force  is 
operating.  Let  us  examine  the  case  of  a  freely  falling  body, 
and  see  how  we  recognize  the  presence  of  the  force  which 
we  call  its  weight. 

Ask  some  one  to  drop  a  good-sized  white  stone  or  ball  from  a  high 
window,  signaling  to  you  the  exact  instant  of  dropping  it,  while  you 
stand  at  some  distance  and  watch  its  fall.  Have  the  experiment  re- 
peated, until  you  become  accustomed  to  the  motion  of  the  object,  so 
that  you  can  observe  it  well. 

You  will  soon  see  that  the  motion  is  accelerated.  The  ball  at  the 
start  moves  very  slowly  (you  must  observe  closely  to  see  this),  but  rapidly 
gains  speed,  and  during  the  latter  part  of  the  fall  moves  so  fast  that 
you  can  hardly  follow  it  with  your  eye.  Thus,  the  motion  is  acceler- 
ated, not  only  at  the  start,  but  throughout  the  fall.  Hence  there  must 
have  been  a  force  (and  therefore  energy)  acting  throughout  the  fall 
Moreover,  as  the  ball  started  from  a  condition  of  rest,  without  effort 
of  the  person  holding  it,  and  as  it  will  start  at  any  desired  instant, 
there  must  be  a  force  acting  always  upon  it. 

As  the  experiment  will  succeed  at  all  times,  in  all  places,  and  with 
all  objects  except  feathers,  etc.,  whose  motion  is  prevented  by  buoyan- 
cy or  other  known  causes,  we  may  generalize,  and  say  that  all  objects 
near  the  earth  appear  to  be  always  acted  upon  by  a  force  (caused  by 
energy  of  some  kind)  drawing  them  toward  the  earth.  This  force  is 
what  we  call  Weight.  As  before  stated,  it  is  a  force  acting  between 
the  earth  and  the  object — i.  e.,  tending  to  make  the  earth  and  the 
object  approach  each  other. 


BALANCED  FORCES.  47 

Weight  is,  therefore,  a  force  which  acts  always  on  all 
objects  near  the  earth.  That  everything  has  weight,  is  one 
of  the  most  familiar  facts  of  our  common  knowledge. 

Forces  recognized  by  means  of  a  Counterbalanc- 
ing Force. — We  naturally  ask  whether  there  are  not  some 
means  of  recognizing  the  existence  of  a  force  without  allow- 
ing acceleration  to  occur.  The  answer  is  that  there  are.  To 
show  what  the  means  are,  we  have  first  to  show  that  forces 
can  be  balanced  or  neutralized  by,  and  only  by,  other  forces. 

Balanced  Forces. — If  two  equal  and  opposite  forces  be 
simultaneously  applied  to  a  free  body,  its  motion  will  be  un- 
changed. Two  such  forces  are  called  balanced  forces.  This 
may  be  illustrated  by  the  following  experiment : 

Over  a  pulley,  P,  moving  with  little  friction  (a  round  stick,  such  as 
a  broom-handle  or  even  a  lead-pencil,  will  .answer  very  well),  hang  two 
bodies,  A  and  B,  of  equal  weight,  and  connected  by  a  cord.  Neither 
will  rise  or  fall.  But  A,  for  example,  is  pulled 
downward  by  a  force  (its  weight).  Why  is  it  not 
accelerated  f  B  by  its  weight  pulls  downward  on  the 
part  of  the  cord  at  D.  This  portion  of  the  cord  pulls 
on  the  part  next  beyond,  and  this  in  turn  on  the  next 
section,  and  so  on  around  to  C,  where  the  cord  pulls 
upward  on  A  by  the  same  amount  (neglecting  fric- 
tion) that  B  pulls  downward.  But  B  pulls  with  an 
amount  equal  to  its  weight,  and  this  is  equal  to  the 
weight  of  A.  Hence,  A  is  pulled  upward  with  a  force  just  equal  to 
its  weight,  and  exactly  opposite  in  direction.  The  acceleration  of  A 
which  would  have  been  produced  by  its  weight  is  thus  prevented  by 
the  application  of  an  equal  and  opposite  force.  The  upward  pull  on 
A  by  the  string,  and  the  weight  of  A,  are  then  two  balanced  forces. 
The  same  statement  is  true  of  B.  The  balanced  forces,  therefore,  can 
not  start  the  bodies. 

If  you  push  up  on  A  or  B,  the  whole  system  will  be  set  in  motion. 
When  you  stop  pushing,  all  acceleration  will  cease,  and  the  motion 
would  continue  uniform,  if  it  were  not  for  friction,  showing  that  the 
balanced  forces  can  not  change  the  speed  of  the  bodies  when  moving. 

Make  the  weight  B  a  little  greater  than  A.  Then  the  upward 
force  on  C  will  be  greater  than  the  downward.  Notice  that  A  will  be 


48  FORCE. 

started  upward — that  is,  in  the  direction  of  the  unbalanced  portion  of 
the  force.  Similarly,  if  the  weight  B  be  made  smaller  than  A,  the  ex- 
cess of  force  will  be  in  the  opposite  direction,  and  A  will  move  down. 
In  each  case  the  force  has,  of  course,  to  accelerate  both  A  and  B,  and 
both  move  in  the  direction  of  the  greatest  force  upon  them. 

From  these  and  similar  experiments  we  may  conclude 
that,  to  prevent  acceleration  in  a  body  which  is  acted  upon 
by  a  force,  there  must  be  applied  an  equal  force  in  an  exact- 
ly opposite  direction. 

Suppose,  therefore,  we  find  at  any  time  a  body  which  we 
know  is  acted  upon  by  a  force,  and  which  is  not  being  accel- 
erated. Then  we  know  that  the  body  is  also  being  acted 
upon  by  a  force  equal  and  opposite  to  the  first.  Even  if 
the  body  is  being  accelerated,  the  acceleration  may  be  due 
to  some  unbalanced  part  of  all  the  forces  acting  upon  it,  and 
may  not  be  the  result  of  a  single  force  only. 

This  affords  us  a  means  of  recognizing  the  existence  of 
forces,  without  allowing  the  acceleration  to  be  produced. 
Anything  which  can  be  balanced  against  any  known  force 
must  itself  be  a  force.  We  have  one  convenient  recognized 
force  to  begin  with,  viz.,  Weight. 

QUESTIONS.— What  is  meant  by  tendency  to  acceleration  ?  To  what  must  such  a 
tendency  always  be  due  ?  Give  an  example  of  a  brief  tendency  to  acceleration. 
Of  a  continuous  one.  Can  a  tendency  continue  after  the  energy  causing  it  has 
ceased  to  act  ? 

What  is  denoted  by  the  term  Force  ?  Define  force.  To  what  is  force  always  due  ? 
Can  there  be  any  force  where  there  is  no  energy  ?  What  is  the  sole  cause  of 
force  ?  Can  force  exist  by  itself  ?  Are  force  and  energy  the  same  thing  ? 
Would  it  ever  be  correct  to  use  one  term  for  the  other  ?  Why  do  we  speak  of 
the  effects  of  energy  upon  bodies  as  the  effects  of  the  force  (i.  e.,  the  tendency 
to  acceleration)  which  the  energy  produces  ?  Is  force  ever  the  real  cause  of 
any  effect  ?  Why  not  ?  What  is  the  cause  ?  What  do  we  mean  by  the  term 
line  of  action  of  a  force  ?  What  is  the  direction  of  the  line  of  action  of  weight  ? 
Give  some  examples  of  forces.  Is  it  found  that  a  force  ever  acts  on  only  a 
single  particle  of  matter  ? 

In  what  two  ways  may  we  recognize  the  presence  of  a  force  ?  Protfe  that  weight 
is  always  acting  upon  any  object  near  the  earth.  What  is  weight  ?  Is  it  en- 
ergy ?  Is  it  due  to  energy  ?  To  what  particular  kind  of  energy  is  it  due  ?  If 
we  see  a  body  moving  with  retarded  motion,  how  do  we  know  that  it  is  being 
acted  upon  by  a  force  ?  How  do  we  know  that  a  body  which  is  being  acceler- 
ated or  retarded  is  being  acted  upon  by  energy  ?  Why  do  we  speak  of  the 
same  case  of  acceleration  sometimes  as  due  to  force,  sometimes  as  due  to  en- 
ergy, and  yet  say  that  energy  and  force  are  not  the  same  thing  ? 


EXAMPLES  OF  FORCES. 


49 


What  is  meant  by  balanced  forces  ?  Give  an  illustration  of  two  forces  balancing 
each  other  ?  How  can  we  prevent  the  acceleration  of  a  body  acted  upon  by  a 
force  ?  Is  there  any  other  way  ?  If  we  find  a  body  which  we  know  to  be  acted 
upon  by  a  force,  but  which  is  not  moving,  what  inference  do  we  draw  ?  How 
does  this  enable  us  to  recognize  other  forces  ? 


EXAMPLES  OF  FORCES. 

Elasticity. — When  objects  are  stretched,  compressed, 
bent,  or  twisted,  they  tend,  as  a  rule,  to  spring  back  to  their 
original  or  normal  size  and  shape.  A  continuous  force  is 
necessary  to  prevent  their  doing  so.  If  the  objects  are 
stretched  or  compressed  too  much,  they  take  up  permanently 
a  stretched,  compressed,  or  bent  shape ;  but  with  this  per- 
manent change  we  are  not  at  present  concerned.  The  prop- 
erty of  tending  to  resume  the  normal  size  or  shape  is  called 
Elasticity.  It  is  due  to  forces  which"  are  brought  into  action 
by  the  change  in  size  or  form.  These  are  known  as  elastic 
forces,  or  forces  of  elasticity. 

Elasticity  of  Stretch. — A  force  due  to  Elasticity  of 
Stretch,  or  Extension,  is  exhibited  by  all  solids 
when  under  stretch. 


Fasten  a  rubber  band  to  a  nail  or  hook  in  the  wall. 
Attach  to  the  lower  end  of  the  band  a  stone  or  any 
convenient  object  (Fig.  13).  What  occurs?  The  band 
stretches  by  a  certain  amount,  and  then,  if  strong 
enough  not  to  break,  stops,  holding  the  body  up  from 
falling.  Mark  two  points  on  the  band  with  a  piece  of 
chalk,  one  near  each  end,  and  measure  their  distance 
apart  when  the.  object  is  hanging  on  the  band.  Take 
off  the  object  and  hang  it  on  again.  Measure  once 
more  the  distance  of  the  points  apart.  Try  the  experi- 
ment on  another  day,  in  another  place,  and  under  a 
variety  of  conditions.  You  will  find  that  the  band  is 
always  stretched  equally  by  the  same  object.  If  you 
use  a  lighter  object,  the  stretch  will  be  less;  if  a 
heavier  one,  it  will  be  greater. 


FIG.  13. 


50  FORCE. 

The  Object  hung  on  the  Band  has  Weight,  which 
is  prevented  from  producing  acceleration  after  the  band  has 
stretched  to  a  certain  amount.  The  weight  must,  there- 
fore, be  counterbalanced  by  an  equal  and  opposite  force. 
The  rubber  band  must  pull  upward  just  as  strongly  as  the 
object  pulls  downward.  The  particles  of  the  rubber,  when 
stretched  from  their  original  positions,  show  a  tendency  to 
return.  This  force  is  greater  the  more  the  band  is  stretched, 
and  is  zero  when  the  band  is  not  stretched  at  all.  It  is 
therefore  a  force  which  is  called  into  action  more  and  more 
strongly  as  the  particles  of  the  rubber  are  pulled  farther 
apart,  and  it  is  due  to  the  elasticity  of  stretch.  It  is  exhib- 
ited by  all  solids,  and  to  some  extent  by  liquids. 

Instead  of  a  rubber  band,  use  a  spiral  spring.  It  will  be  stretched 
in  a  similar  way ;  but  this  is  really  a  case  of  combined  bending  and 
twisting.  Or  use  a  string,  a  straight  wire,  a  glass  rod,  or  a  piece  of 
any  solid  substance,  either  large  or  small.  It  will  be  stretched  just  as 
the  band  was ;  but  you  will  not  easily  discover  the  fact,  for  the  stretch 
will  be  so  small  that  it  can  not  easily  be  appreciated.  With  proper 
apparatus,  however,  it  can  be  seen  and  even  measured. 

Elasticity  of  Compression. — A  force  due  to  Elasticity 
of  Compression  is  exhibited  by  all  solids,  liquids,  and  gases, 
when  compressed. 

Place  a  thick  piece  of  rubber  on  the  table.  Lay  a  heavy  object  on 
the  rubber.  Notice  that  the  thickness  of  the  rubber  is  made  less.  If 
in  place  of  the  rubber  we  were  to  use  any  other  object  strong  enough 
not  to  break,  it  would  be  similarly  in  a  state  of  compression  and  would 
be  exerting  a  force  due  to  elasticity  when  the  object  rested  upon  it. 
The  compression  can  sometimes  be  seen,  as  in  the  case  of  rubber,  but 
is  often  so  slight  as  to  require  delicate  apparatus  to  measure  it. 

As  the  acceleration  which  the  weight  would  produce  is 
prevented,  the  compressed  solid  must  be  exerting  a  force 
equal  and  opposite  to  the  weight  of  the  object.  The  particles 
of  the  rubber  are  brought  nearer  together  and  show  a  tend- 
ency to  move  back  to  their  original  positions.  This  tend- 
ency constitutes  the  force  of  elasticity  of  compression, 


ELASTICITY.  51 

Elasticity  of  Bending. — When  a  solid  is  bending,  the 
forces  of  elasticity  of  stretch  and  compression  are  both  ex- 
hibited. 

Fasten  one  end  of  a  long,  slender  rod  of  wood  (about  a  yard  in 
length  and  half  an  inch  on  a  side)  to  a  table  by  means  of  a  clamp  or 
nails.  Hang  a  heavy  object  on  the  end.  This  end  will  move  down- 
ward to  a  certain  point,  and  after  a  few  vibrations  will  come  to  rest 
there.  The  rod  will  be  bent  into  a  curved  form.  In  this  condition 


FIG.  14.— ILLUSTRATING  ELASTICITY  OF  BENDING. 

the  upper  layers  of  the  wood  (convex  side)  are  in  a  condition  of  stretch ; 
the  lower  layers  (concave  side)  are  in  compression.  You  can  illustrate 
this  by  bending  a  twig  in  your  hand  and  examining  the  appearance  of 
the  upper  and  lower  sides  as  you  bend  it.  The  elastic  forces  called 
into  play  in  bending  are  those  of  compression  and  stretch. 

Elasticity  of  Torsion  or  Twisting. — When  any  solid 
is  twisted,  it  exhibits  a  force  due  to  Elasticity  of  Torsion. 

Take  hold  of  the  end  of  the  wooden  rod  of  the  last  experiment, 
after  removing  the  weight.  Twist  the  rod  without  bending  it.  The 
more  you  twist  it,  the  greater  force  you  have  to  exert.  When  you  let 
go  your  hold,  the  wood  untwists.  The  operation  of  twisting  changes 
the  relative  positions  of  the  particles,  which,  when  thus  treated,  show 
a  tendency  to  return  to  their  original  positions.  This  is  another  exhi- 
bition of  elastic  force,  and  is  called  elasticity  of  torsion. 

All  Elasticity  is  of  the  Same  Kind,  although  ap- 
pearing in  somewhat  different  ways.  It  is  doubtless  due  to 
some  form  of  energy  which  gives  the  molecules  a  tendency 
to  move  toward  one  another  when  they  are  separated,  or 
away  from  one  another  when  they  are  crowded  together  by 


52  FORCE. 

the  action  of  force  applied  to  the  body.     As  to  just  what 
this  form  of  energy  is,  nothing  is  known. 

In  the  examples  of  elasticity,  the  force  applied  to  produce  the 
stretch,  compression,  etc.,  was  the  weight  of  some  object.  That  force 
was  used  merely  for  convenience ;  any  other  might  have  been  em- 
ployed. For  instance,  we  might  hang  on  the  rubber  band  a  piece 
of  iron ;  the  band  will  be  stretched  to  hold  the  weight  of  the  iron.  If 
the  magnet  be  now  brought  up  beneath  the  iron,  the  band  will  be 
further  stretched  by  the  action  of  magnetic  force  between  the  iron 
and  the  magnet. 

We  must  remember  also  that  the  band  when  hanging  is  somewhat 
stretched  by  its  own  weight  alone ;  similarly,  the  block  of  rubber  is 
compressed  and  the  wooden  rod  bent  slightly  by  their  own  weights. 

From  these  experiments,  and  others  of  the  same  nature, 
it  follows  that  whenever  we  see  any  object  under  Stretch, 
Compression,  Bending,  or  Twisting,  we  may  be  sure  that  a 
force  due  to  elasticity  is  being  exerted.  Thus  we  have 
added  these  to  our  list  of  recognized  forces,  and  can  use 
them  in  turn  as  a  means  of  recognizing  others. 

Think  out  for  yourself  how  the  table  is  compressed  when  an  object 
is  laid  upon  it ;  how  the  hook  is  bent  upon  which  the  rubber  band  is 
hung;  how  the  floor  bends  when  you  walk  over  it;  how  a  bridge 
yields  when  a  heavy  load  crosses  it,  as  also  under  its  own  weight ;  and 
any  other  cases  of  stretching,  compression,  bending,  and  torsion,  which 
may  occur  to-  you.  Try  in  each  of  them  to  recognize  the  fact  that  an 
elastic  force  is  being  exerted. 

Forces  occur  under  various  conditions  of  matter. 
They  are  not  indestructible  in  the  sense  that  matter  and 
energy  are,  but  may  be  made  larger  or  smaller  in  amount  or 
in  many  cases  annihilated  altogether. 

Always  remember  that  force  is  merely  a  condition  oi 
matter  which  is  due  to  the  action  of  energy.  When  we  find 
a  force,  we  at  once  inquire  what  the  energy  causing  the  force 
is.  This  question  we  can  answer  definitely  in  a  few  cases 
only.  In  most  instances,  our  knowledge  of  the  exact  nature 
of  the  motion  causing  different  forms  of  energy  is  very  in- 
complete. A  few  other  examples  of  forces  will  now  be 


FORCES  OF  ATTRACTION  AND  REPULSION. 


53 


given,  especial  attention  being  called  to  the  fact  that  at 
least  two  bodies  are  concerned  in  every  force. 

Electric  Attraction  and  Repulsion. — Suspend  two 
pith-balls  from  glass  rods  or  tubes  mounted  in  wooden 
blocks,  as  shown  in  Fig.  15,  using  very  fine  silk  thread  (un- 
dyed  floss  or  cocoon-fiber  is  best). 

Touch  the  balls  with  the  fingers  to  remove  all  electrification.  They 
will  then  hang  straight  down  as  at  a  and  b,  with  the  threads  vertical. 
There  is  no  electric  force  between  them ;  they  do  not  tend  to  ap- 
proach, or  recede  from,  each  other. 

Now,  electrify  a  by  bringing  against  it  a  piece  of  vulcanite  which 
has  been  briskly  rubbed  on  dry  silk  or  fur,  and  thus  electrified.  By 
allowing  a  to  roll  over  the  rubbed  surface  several  times,  it  will  become 
thoroughly  electrified. 
Take  care  that  b  does 
not  touch  the  vulcan- 
ite, or,  if  it  has  done 
so,  hold  it  for  a  mo- 
ment in  the  fingers  to 
remove  the  charge  of 
electricity.  Then  move 
the  stands  up  toward 
each  other,  as  in  the 
figure.  The  threads 
will  no  longer  hang 
vertical,  but  the  balls 
will  move  toward  each 
other  and  hang  in  the 
positions  c  and  d  in- 
stead of  a  and  b.  This 
shows  that  there  is  a 

tendency  for  a  and  b  to  be  accelerated  toward  each  other — that  is,  that 
there  is  a  force  of  attraction  between  them.  The  ball  a  was  the  one 
electrified ;  but  the  force  due  to  its  electrified  condition  is  not  simply 
a  tendency  of  a  to  move  toward  J,  or  of  b  to  move  toward  a,  but  it  is 
a  tendency  of  both  a  and  b  mutually  to  approach  each  other. 

Next  roll  each  of  the  balls  in  the  fingers  for  a  moment ;  they  will 
then  hang  in  their  original  vertical  positions  without  attraction  or  re- 
pulsion. Thus  we  have  been  able  to  produce  force  and  to  destroy  it 


d 


FIG.  15.— ATTRACTION  AND  REPULSION  OF  PITH  BALLS. 


54  FORCE. 

Electrify  both  balls  by  touching  them  with  the  rubbed  vulcanite, 
and  bring  them  toward  each  other.  They  will  now  tend  to  move  apart 
and  will  hang  in  the  positions  e  and  /,  showing  that  there  is  a  repul- 
sive force  between  them.  Other  interesting  experiments  with  the 
pith-balls  will  be  suggested  when  the  subject  of  electricity  is  reached. 

Magnetic  Attraction. — Provide  yourself  with  a  mag- 
net and  a  nail.  Bring  the  nail  and  one  end  of  the  magnet 
gradually  toward  each  other.  When  they  are  near  together, 
you  will  feel  that  they  tend  to  approach ;  you  will  have  to 
hold  each  back,  or  they  will  rush  together.  There  is,  then, 
a  force  of  attraction  between  them,  and  this  force  is  greater 
the  nearer  they  come  together,  being  imperceptible  at  a  dis- 
tance of  a  few  inches.  It  is  called  magnetic  force  or  mag- 
netic attraction,  and  is  due  to  magnetism. 

The  Earth  tends  to  approach  a  Body  as  well  as  a 
body  the  earth.  We  can  not  readily  show  this  by  the 
method  of  watching  their  motions;  but  we  are  very  well 
assured  of  the  fact  by  other  knowledge  which  we  possess 
regarding  similar  actions.  We  know  that  the  moon  re- 
volves around  the  earth,  that  the  earth  and  other  planets 
revolve  around  the  sun,  that  some  stars  form  pairs  revolving 
about  each  other.  For  certain  reasons  we  believe  that  every 
particle  of  matter  tends  to  approach  every  other  particle, 
the  amount  of  the  tendency  depending  on  the  mass  of  the 
two  particles  and  their  distance  apart.  This,  when  fully 
stated,  is  called  the  Law  of  Gravitation. 

Starting  from  this  assumption,  we  must  believe  that  the  earth, 
moon,  sun,  and  all  the  planets,  attract  one  another  with  amounts  de- 
pending on  their  masses  and  their  distances  apart  at  any  given  instant. 
If  there  were  only  one  planet,  it  would  move  about  the  sun  in  a  per- 
fectly regular  path.  If  there  were  two  revolving  at  different  distances 
and  in  different  times,  then  their  motion  would  not  be  perfectly  regu- 
lar, but  when  they  were  near  together  each  would  disturb  the  position 
of  the  other,  now  slowing,  now  increasing,  its  speed,  and  also  moving 
it  more  or  less  aside  from  its  simple  path. 

Imagine  several  planets,  as  in  our  Solar  System,  and  you  will  see 
that  the  irregularity  introduced  into  their  otherwise  simple  motion 


DIRECTION  CHANGED  BY  FORCE. 


55 


must  be  very  complicated.  Their  paths  are  disturbed  by  their  mutual 
actions,  and  the  orbit  of  our  moon  is  particularly  so.  Yet  astrono- 
mers, basing  their  work  wholly  on  the  law  of  gravitation,  are  able  to 
compute  the  position  of  the  moon  for  any  given  time  several  years  in 
the  future.  We  therefore  have  here  a  remarkable  piece  of  evidence 
that  the  assumption  of  the  law  of  gravitation  is  correct;  and  this 
assumption  involves  the  idea  that  at  least  two  bodies  are  necessary  to 
produce  this  kind  of  tendency  to  motion,  and  that  each  of  the  bodies 
concerned  has  an  equal  tendency  to  move  toward  the  other. 


FORCE  CHANGING  DIRECTION  OF  MOTION. 

Effect  of  Force  inclined  to  Direction  of  Moving- 
Body. — In  the  cases  of  balanced  forces,  the  lines  of  action 
of  the  forces  have  been  in  opposite  direc- 
tions. Let  us  see  the  effect  of  force 
inclined  to  the  direction  of  a  body's 
motion. 

Throw  a  ball  in  any  other  direction 
than  a  vertical  one.     It  will  move  in 
a  curved  line.     Suppose  the  ball  to 
start  at  A  and  to  be  thrown  in  the 
direction  of  A  F.     It  would  move 
along  this  straight  line  A  F  at 
a  uniform  rate  if  there  were    C, 
no  tendency  (weight)  to  fall 
toward    the    earth.       The 
weight,  however,  we  know 
was  acting  all  the  time. 
We  find  that  the  ball 
travels  in  a    curved 
path  A  B'  C'  I'. 

If  the  ball  had 

been  thrown   hori-  FIG.  16.— ILLUSTRATING  CHANGE  OF  DIRECTION. 

zontally,  it    would 

have  moved  in  the  path  A  b  c  e  of  Fig.  17.  If  thrown  obliquely  down- 
ward in  the  direction  A  E,  Fig.  17,  it  would  have  moved  in  the  path 
A  B'  C'  D'.  In  all  cases,  the  motion  is  in  a  curved  path.  Notice  that 
the  direction  of  action  of  the  weight,  being  vertically  downward,  is 
always  inclined  to  the  path,  while  in  the  case  of  a  body  moving  verti- 


56 


FORCE. 


cally  upward  or  downward  the  weight  acts  in  the  direction  of  the  path. 

Hence,  when  the  force  acts  in  the  direction  of  the  path,  the  motion  is 
not  changed  in  direction  but  only  acceler- 

A b c  d  e  ated  or  retarded.  When  the  force  is  in- 
clined to  the  path,  the  direction  of  motion 
is  continually  changed. 

It  will  also  be  seen  by  inspection  that 
the  motion  in  the  three  cases  above  is  ac- 
celerated or  retarded  as  well  as  curved; 
but  if  the  force  is  exactly  and  always  at 
right  angles  to  the  path,  the  velocity  is 
uniform,  although  the  direction  is  con- 
tinually changing.  This  is  the  case  of  a 
body  revolving  uniformly  in  a  circle.  It 
may  be  illustrated  by  whirling  around  a 
FIG.  17.  stone  on  the  end  of  a  string. 

QUESTIONS.— What  is  elasticity  ?  What  are  the  forces  of  elasticity  ?  Show  that 
a  stretched  object  exerts  a  force  tending  to  restore  it  to  its  normal  size  and 
shape.  If  a  weight  is  hung  on  any  object  whatever,  is  the  object  stretched  ?  Is 
it  exerting  a  force  ?  Answer  similar  questions  for  compression,  bending,  and 
twisting.  What  is  the  particular  form  of  energy  causing  the  elastic  forces  ? 
As  you  stand  upon  the  floor,  does  the  floor  exert  an  upward  force  against  your 
feet  ?  How  much  force  does  it  exert  ?  To  what  property  of  the  floor  is  the 
force  due  ?  Does  the  floor  push  upward  against  the  table  standing  upon  it  ? 
Why  is  not  the  table  moved  upward  by  this  push  ? 

Does  a  mountain  press  upon  the  earth  beneath  it  ?  If  the  upper  layers  of  the 
earth  press  upon  those  beneath,  what  must  be  the  amount  of  pressure  upon 
layers  several  miles  below  the  surface  ?  When  a  train  passes  on  a  bridge,  how 
much  does  it  press  upon  the  bridge  ?  Can  the  bridge  be  prevented  from  bend- 
ing slightly  ?  How  does  the  bridge  balance  the  weight  of  the  train  ? 

Show  that,  when  an  electrified  pith-ball  hangs  near  another  pith-ball,  the  balls  at- 
tract each  other.  Does  one  attract  more  than  the  other  ?  How  can  you  prove 
that  the  attraction  between  a  magnet  and  iron  is  mutual  ?  Give  reasons  for 
believing  that  weight  is  a  force  pulling  the  earth  and  the  object  toward  each 
other,  and  not  merely  pulling  the  object  toward  the  earth.  When  an  object 
falls,  does  the  earth  move  upward  toward  it  ?  Describe  by  diagram  the  ex- 
periment showing  that  force  changes  the  direction  of  motion  of  a  body. 


PRODUCTION  OF  FORCE  BY  ENERGY. 

Acceleration  and  the  Tendency  to  Acceleration, 

it  must  be  remembered,  are  caused  by  the  action  of  energy, 
and  can  result  from  nothing  else.  This  action  of  energy 
has  already  been  called  Force.  In  order  that  you  may  better 


PRODUCTION   OF   FORCE.  57 

understand  how  it  is  possible  for  energy  to  produce  force, 
and  why  we  believe  that  force  is  wholly  due  to  energy,  con- 
sider carefully  the  following  illustration : 

Hold  a  bat  or  a  board  in  your  hands  and  let  some  one  throw  against 
it  an  elastic  ball.  To  prevent  the  board  from  moving  when  the  ball 
strikes  it,  you  will  have  to  push  against  it.  The  ball  exerts  a  force 
during  impact.  Suppose  a  large  number  of  elastic  balls  to  strike  the 
board  in  rapid  succession.  You  will  then  have  to  exert  a  continuous 
push  to  hold  the  board  steady.  If  the  board  is  held  in  place  by 
springs,  these  springs  will  be  compressed  until  the  pressure  which  they 
exert,  owing  to  elasticity,  will  be  just  equal  to  the  pressure  or  force 
caused  by  the  striking  balls.  The  compression  will  be  kept  up  as  long 
as  the  bombardment  of  balls  continues.  It  is  thus  clear  that  a  con- 
tinuous bombardment  of  balls  can  produce  a  sensibly  continuous  force. 

Let  us  see  what  becomes  of  the  Energy  of  the  balls 
when  they  are  producing  force  : 

First,  when  the  board  is  stationary.  If  we  had  suitable 
means  of  measuring,  we  should  find  (provided  board  and 
balls  were  perfectly  elastic)  that  the  balls  rebound  with  just 
the  velocity,  and  therefore  just  the  energy,  with  which  they 
strike.  They  therefore  lose  no  energy  when  producing  force 
if  the  body  acted  upon  is  stationary.  The  mere  production 
of  force  does  not  require  the  expenditure  of  energy.  The  only 
change  made  is  in  the  direction  of  motion  of  the  balls. 

Secondly,  when  the  balls  are  allowed  to  accelerate  the 
board.  Again,  if  we  could  measure,  we  should  find  that 
when  the  board  is  moving  in  the  direction  in  which  the 
balls  tend  to  make  it  move,  they  will  rebound  with  less 
velocity  than  that  with  which  they  strike,  and  therefore 
with  less  energy.  They  are  thus  giving  up  energy  to  the 
board,  which,  if  free  to  move,  will  be  accelerated  just  as  was 
the  ball  B  (page  31).  The  acceleration  of  the  board  will  be 
such  that  it  will  gain  energy  at  just  the  rate  at  which  the 
striking  balls  lose  it.  The  energy  expended  by  the  balls  is 
simply  transferred  or  given  up  to  the  board.  The  force  ex- 
ists as  before,  but  no  energy  is  expended  in  maintaining  it. 


58  FORCE. 

We  thus  see  how  energy  like  that  of  the  bombarding  balls 
can  accelerate  a  body — i.  e.,  can  do  work. 

Thirdly,  when  the  board  is  pushed  back  against  the 
balls.  Here  the  same  amount  of  force  exists  as  in  both  the 
other  cases;  but  now  each  striking  ball  rebounds  with 
greater  velocity  than  that  with  which  it  strikes,  and  there- 
fore gains  energy.  To  push  the  board  back  will  require  an 
application  of  energy,  which  is  transferred  to  the  system  of 
balls  in  the  shape  of  increased  energy  of  motion. 

Fourthly,  where  the  board  is  allowed  to  be  moved  back 
by  the  balls  with  a  uniform  motion.  In  this  case  the  force 
will  be  present  as  before.  The  balls  will  also  rebound  with 
less  than  their  striking  velocity,  and  will  therefore  give  up 
energy  to  (i.  e.,  do  work  upon)  the  board ;  but  as  the  board 
is  moving  with  a  uniform  velocity,  it  is  not  accumulating 
energy  as  in  the  second  case.  The  energy  here  can  simply 
be  transmitted  through  the  board  to  some  other  object. 

In  all  these  cases,  if  we  had  merely  seen  the  compression  of  the 
springs  or  felt  that  we  were  obliged  to  push,  and  had  been  ignorant  or 
unconscious  of  the  energy  on  the  other  side  of  the  board,  we  should 
have  been  aware  only  of  a  condition  which  we  have  already  recognized 
in  other  cases  as  due  to  force.  We  should  naturally,  therefore,  have 
spoken  of  the  force  as  causing  the  acceleration,  doing  the  work,  and 
being  worked  against ;  but  it  is  evident  that  such  a  statement  would 
have  been  imperfect.  This  illustrates  the  position  we  are  in  respecting 
weight,  elasticity,  etc.  We  perceive  the  force  by  methods  already 
given,  but  are  ignorant  of  the  exact  nature  of  its  cause.  We  speak  of 
weight  and  other  forces  as  doing  work,  while  the  real  agent  is  energy 
of  some  kind  which  is  causing  the  force  in  question. 

The  illustration  just  given  is  a  purely  imaginary  one,  although  en- 
tirely practicable ;  but  we  have  in  nature  a  force  which  is  explained 
on  precisely  this  principle.  It  will  be  shown,  when  gases  are  treated, 
that  a  gas,  for  example  air,  in  an  inclosed  space,  exerts  an  outward 
pressure  upon  all  the  inclosing  walls.  This  pressure  is  explained  as 
being  due  to  the  bombardment  of  the  walls  by  the  molecules  of  the 
gas  in  their  violent  to-and-fro  motions  described  on  page  37. 

We  are  not,  of  course,  to  assume  that,  because  the  bombarding 
balls  enable  us  to  perceive  how  energy  may  and  sometimes  does  cause 


PRODUCTION  OF  FORCE.  59 

force,  therefore  all  force  is  produced  by  just  such  a  process.  It  is 
probable  that  this  is  not  true,  but  that  the  form  of  the  energy  causing 
such  forces  as  weight,  elasticity,  magnetic  and  electrical  attraction, 
etc.,  is  or  may  be  very  different  from  a  process  of  bombardment. 

The  argument  from  which  results  the  belief  that  force 
is  always  caused  by  energy  is — first,  that  it  is  strictly  in 
accordance  with  the  principle  of  the  conservation  of  energy 
(page  39) ;  second,  that  it  leads  us  into  no  contradiction 
with  observed  facts  of  any  kind,  but,  on  the  contrary,  en- 
ables us  to  explain  many  facts  that  can  not  be  so  well 
accounted  for  in  any  other  way. 

QUESTIONS.— Define  force.  On  what  only  does  it  depend,  and  in  what  does  it  al- 
ways manifest  itself  ?  Give  an  illustration  showing  that  energy  is  the  cause  of 
force,  and  that  force  is  wholly  due  to  energy.  Do  we  understand  the  source  of 
every  manifested  force  ?  Why  ?  Does  the  production  of  force  require  the  ex- 
penditure of  energy  ?  In  pushing  a  board  back  against  striking  balls,  what 
becomes  of  the  energy  applied  ?  Sum  up  the  four  cases  in  which  the  energy 
of  striking  balls  produced  force,  and  explain  the  transfer  of  energy  in  each. 
In  these  cases,  had  we  been  ignorant  of  the  "energy,  to  what  would  we  have 
ascribed  the  visible  effects  ?  State  a  parallel  case  from  the  properties  of  gases. 
Can  we  assume  that  all  force  is  similarly  caused  ?  Advance  the  argument 
from  which  results  the  belief  that  all  force  is  produced  by  energy. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

Throw  a  ball  straight  upward.  Is  its  condition  the  same  going  up  as  coming 
down  ?  In  what  respect  is  there  a  difference  ?  Does  the  same  tendency  of  ac- 
celeration toward  the  earth  exist  in  both  cases  ?  Does  the  ball  weigh  the  same 
whether  moving  upward  or  downward  ? 

Prop  up  a  smooth  board  on  the  floor  and  lay  a  marble  on  the  elevated  end.  Re- 
lease the  marble,  and  as  it  rolls  down  the  board  what  will  it  show  ?  Draw  chalk- 
marks  across  the  board  at  equal  intervals,  and  you  will  perceive  the  change  of 
speed  more  readily.  To  what  is  the  motion  of  the  ball  here  due  ? 

Hang  up  the  rubber  band  as  explained.  Fasten  to  its  lower  end  a  small  piece 
of  iron.  The  band  will  stretch  slightly  till  its  elastic  force  balances  the 
weight  of  the  iron.  Now  bring  your  magnet  carefully  up  under  it.  The  band 
will  stretch  further,  showing  a  stronger  pull  by  the  iron  than  that  due  to  its 
weight.  If  the  magnet  is  brought  close  enough,  the  iron  will  be  pulled  up  into 
contact  with  it.  Then,  if  you  pull  downward,  you  will  find  that  the  band  is 
stretched  considerably,  and  may  even  break  before  the  iron  can  be  separated 
from  the  magnet.  Does  the  rubber  exert  a  counterbalancing  force  ?  How  ? 

Hang  your  magnet  on  the  rubber  band  and  then  bring  a  nail  up  toward  it.  The 
band  will  be  stretched.  What  does  this  show  ?  Can  the  force  exist  unless 
both  bodies  are  present  ? 

With  a  horizontal  wind,  your  kite  rises.  Draw  a  diagram  showing  the  action  of 
the  forces  in  operation. 


"^  • 


PROPERTIES  AND  CONSTITUTION 
OF  MATTER. 


ESSENTIAL  PROPERTIES. 

By  the  Study  of  Material  Objects  it  is  found  that 
they  possess  certain  characteristics  called  properties. 

The  Essential  Properties  of  Matter. — Some  of  these 
properties  characterize  all  objects  in  common — that  is,  if 
any  object  whatever  be  examined,  it  will  be  found  to  have 

NOTE. — In  the  picture  above  are  represented  a  number  of  simple  pieces  of  ap- 
paratus, with  the  help  of  which,  together  with  such  contrivances  as  may  easily 
be  improvised  from  materials  found  in  every  household,  the  pupil  can  perform  for 
himself  the  experiments  described  in  the  following  sections  on  the  Properties  of 
Matter,  Dynamics,  Gravitation,  and  Machines  :  No.  1  represents  a  wooden  wag- 
on, with  pulley  and  scale-pan  ;  2,  a  grooved  board  with  ivory  balls  ;  3,  a  pulley 
and  weights  ;  4,  a  pole  with  weights  supported  by  spring-balances  ;  5,  apparatus 
for  equilibrium  of  moments  of  forces  tending  to  produce  rotation  ;  6,  a  piece  of 
cardboard  hanging  on  a  pin,  with  plumb-line  in  front,  for  finding  center  of  grav- 
ity ;  7,  a  block  of  wood,  with  string  attached  to  slide  on  board,  for  illustrating 
the  laws  of  friction  ;  8,  a  balance  ;  9,  pendulums  ;  10,  pulleys  of  different  varie- 
.ties.  This  apparatus  may  be  largely  constructed  by  any  ingenious  pupil  who  can 
handle  carpenter's  tools,  or  the  outfit  may  be  obtained  from  any  reputable 
dealer  in  optical  and  philosophical  instruments. 


MASS  AND  EXTENSION.  61 

them.  Moreover,  in  whatever  way  it  is  treated,  whether  it 
is  chemically  separated  into  its  constituents  or  combined 
into  other  compounds,  the  resulting  substances  will  still 
show  these  properties.  So  far  as  we  can  perceive,  they  be- 
long to  any  portion  of  matter,  however  small,  even  to  a 
single  atom.  Thus  they  appear  to  be  properties  of  the  mat- 
ter of  which  objects  are  made  up,  and,  as  far  as  human 
knowledge  extends,  there  is  no  form  of  matter  which  does 
not  possess  them.  These  essential  properties  are  Mass,  Ex- 
tension, Impenetrability,  Indestructibility,  and  Inertia. 

There  are  certain  other  properties  which  appear  to  belong  to  bodies 
(collections  of  atoms),  but  not  to  be  essential  to  matter  itself,  and  there- 
fore not  to  characterize  single  atoms.  Some  of  these  Properties  of 
Bodies,  such  as  Density,  Divisibility,  and  Porosity,  are  merely  facts  or 
hypotheses  concerning  the  structure  of  bodies.  Others,  like  Hard- 
ness, Ductility,  Transparency,  Electric  Conductivity,  relate  to  the 
qualities  which  the  bodies  show  when  treated  in  certain  ways.  Still 
others,  like  Gravitation,  Cohesion,  Elasticity,  etc.,  are  conditions  of 
matter  due  to  the  action  of  energy.  It  is  useless  to  attempt  to  enu- 
merate all  these  properties  of  bodies  ;  they  will  be  considered  one  by 
one  as  the  study  of  the  subject  progresses. 

Mass. — If  you  were  to  ask  how  much  of  a  certain  mate- 
rial substance  existed,  and  the  reply  were  made  none,  you 
would,  of  course,  understand  that  the  substance  did  not  ex- 
ist. By  the  question  "  how  much,"  you  mean  what  quan- 
tity. The  property  of  having  quantity  is  therefore  essential 
to  matter ;  but  the  term  mass  stands  simply  for  quantity  of 
matter  (page  11).  So  we  may  say  that  mass  is  an  essential 
property  of  matter. 

Extension  is  the  property  of  occupying  space,  or,  in 
other  words,  of  having  volume  (length,  breadth,  and  thick- 
ness). "We  recognize  easily  that  almost  every  material  ob- 
ject has  length,  breadth,  and  thickness,  and  thus  occupies 
or  fills  up  more  or  less  completely  a  portion  of  space.  Some 
objects  are  so  small  that  we  can  not  see  them  with  the  un- 
aided eye ;  but  it  is  impossible  to  think  of  them  as  not  hav- 


62       PROPERTIES  AND  CONSTITUTION  OF  MATTER. 

ing  volume.  So  accustomed  are  we  to  this  idea,  that,  if  any 
one  were  to  say  that  a  body  occupied  no  space,  we  should 
declare  at  once  that  it  did  not  exist. 

Many  things  which  are  too  small  for  us  to  appreciate  with  the  eye 
can  be  seen  with  a  magnifier.  We  have  reason  to  believe  that 
there  are  other  objects  too  small  to  be  seen  even  with  the  most  pow- 
erful microscope,  yet  we  realize  that  they  occupy  a  minute  portion 
of  space.  We  know  that  some  things  are  so  thin  that  they  seem  to 
have  no  sensible  thickness  ;  but  if  we  imagine  many  hundreds  or  thou- 
sands of  them  piled  together,  we  may  be  sure  that  they  will  have  a 
perceptible  thickness.  Thus,  gold-leaf  is  so  thin  as  to  appear  of  no 
sensible  thickness  to  the  touch ;  but  if  several  hundred  thousand 
sheets  of  it  were  piled  one  upon  another,  the  whole  would  have  a 
thickness  of  an  inch  or  more  This  shows  that  each  sheet  has  thick- 
ness. The  idea  of  occupying  space  is  thus  one  which  is  inseparably 
associated  with  our  idea  of  matter.  We  can  not  conceive  of  any  por- 
tion of  matter,  however  minute,  which  would  not  have  some  volume. 

Impenetrability. — We  have  seen  that  matter  occupies 
space.  We  also  believe  that  no  two  atoms  of  matter  can 
occupy  the  same  portion  of  space  at  the  same  time.  It  has 
been  further  shown  that  the  molecules  or  atoms  of  matter 
are  probably  never  packed  solidly  together,  but,  on  the  other 
hand,  have  always  spaces  between  them.  When  we  say, 
then,  that  no  two  atoms  can  occupy  the  same  space  at  the 
same  time,  we  do  not  mean  to  apply  the  statement  to  mate- 
rial objects  or  bodies  composed  of  many  atoms.  The  atoms 
of  two  bodies  can  not  occupy  the  same  actual  portion  of 
space  ;  but  the  atoms  of  one  body  may  lie  in  the  spaces  be- 
tween the  atoms  of  the  other,  so  that  two  bodies  may 
have  just  the  same  apparent  volume  as  one.  This  will  be 
more  fully  explained  in  the  section  on  Porosity. 

To  illustrate  impenetrability,  take  any  object,  such  as  a  stone  or 
a  piece  of  wood.  Varnish  it,  if  necessary,  to  keep  water  from  entering 
its  cavities ;  immerse  it  in  a  tumbler  full  of  water.  The  water  will 
overflow,  being  displaced  by  the  object.  The  volume  of  the  displaced 
water  will  be  exactly  equal  to  that  of  the  immersed  solid.  Invert  a 
tumbler ;  force  it  mouth  downward  into  a  dish  of  water.  The  water 


CONSERVATION  OF  MATTER.  63 

does  not  enter,  because  of  the  air  in  the  tumbler.  The  air  acts  as  a 
solid,  except  that  it  is  somewhat  compressed  by  the  water  pressure,  as 
you  will  see  on  examination.  These  experiments  illustrate  the  familiar 
statement  that  two  bodies  "  can  not  occupy  the  same  space  at  the  same 
time."  But  the  true  idea  of  impenetrability  has  reference  to  the 
atoms  of  matter  rather  than  to  bodies. 

Indestructibility. — Conservation    of  Matter. — The 

fact  that  matter  is  indestructible  can  not  easily  be  proved  at 
this  stage  of  our  studies.  The  assertion  must  be  accepted 
as  true,  although  seemingly  contrary  to  experience. 

Stand  a  tumbler  of  water  on  the  table  and  leave  it  for  a  day  or  two. 
The  water  disappears  gradually,  and  you  can  not  see  what  has  become 
of  it.  It  appears  to  have  been  destroyed ;  but  it  has  only  passed  off 
into  the  air  in  the  form  of  invisible  vapor  The  vapor  is  still  the  same 
substance  as  the  water ;  the  molecules  of  the  water  vapor  and  of  the 
liquid  water  are  exactly  the  same.  The  difference  between  the  vapor 
and  liquid  is  only  that  the  molecules  in  the  vapor  are  very  much 
farther  apart  than  in  the  liquid  (a  cubic  inch  of  the  liquid  water  mak- 
ing over  60,000  cubic  inches  of  vapor  at  the  ordinary  room  tempera- 
ture). Thus  the  vapor  can  not  be  distinguished  by  the  eye  from  the 
air  of  the  room. 

Now,  how  can  we  tell  that  the  water  still  exists  in  the  air  ?  Take  a 
tumbler  of  ice-water,  or,  better,  a  piece  of  glass,  a  spoon,  or  any  object 
which  has  been  lying  in  some  very  cold  place.  Wipe  it  dry  on  the 
outside  without  warming  it,  and  hold  it  just  above  the  water  in  the 
tumbler.  There  will  very  quickly  appear  on  its  surface  a  coating  of 
fine  particles  or  drops  which  you  will  recognize  as  water.  The  cold 
surface  has  collected  the  molecules  of  water  from  the  air  into  the 
liquid  form,  or,  as  we  say,  has  condensed  the  vapor.  You  see  every 
day  a  layer  of  moisture  on  the  pitcher  of  ice- water,  or  on  the  cold  win- 
dow-pane a  coating  of  dew  or  frost.  This  is  water  or  ice,  produced  by 
condensing  from  the  air  of  the  room  the  moisture  or  water  vapor 
which  has  evaporated  from  the  surface  of  water  in  the  room  or  else- 
where. 

When  water  disappears  in  this  way,  then,  it  is  not  destroyed,  but 
merely  changed  into  a  different  condition,  in  which  we  do  not  happen 
to  be  able  to  perceive  it  so  readily.  The  same  change  takes  place 
when  water  boils  away,  when  clothes  dry,  when  ice  and  snow  evapo- 
rate. The  vapor  is  often  condensed  in  the  air  itself,  and  we  see  what 
we  call  rain,  clouds,  mist,  and  fog.  These  are  all  made  up  of  particles 


64       PROPERTIES  AND  CONSTITUTION  OF  MATTER. 

of  liquid  water  more  or  less  fine,  produced  by  the  condensation  of  the 
vapor  as  it  is  chilled  by  some  process  which  happens  to  cool  the  air. 

Another  way  in  which  matter  appears  to  be  destroyed, 
but  is  not,  may  be  studied  in  the  chemical  changes  that  take 
place  in  combustion  or  burning.  Wood  or  coal  when  set  on 
fire  continues  to  burn  until  nothing  is  left  but  ashes.  A 
pile  of  wood  will  leave  an  amount  of  ash  so  small  that  you 
can  lift  it  with  hardly  a  thought  that  it  has  any  weight. 
The  ashes  then  retain  only  a  small  part  of  the  matter 
which  made  up  the  wood.  Where  has  the  rest  of  it  gone  ? 
Has  it  been  destroyed  ?  In  one  sense  it  has,  for  it  no  longer 
exists  as  wood.  A  building  burned  to  the  ground  is  de- 
stroyed as  far  as  its  usefulness  as  a  building  is  concerned. 
But  in  neither  case  has  the  matter  contained  in  the  object 
been  destroyed.  There  is  just  as  much  matter  as  before, 
but  its/orm  has  been  changed. 

The  wood  has  been  converted  partly  into  water  vapor,  partly  into 
invisible  gases,  and  partly  into  ash.  If  we  should  measure  the  mass  of 
the  wood  with  which  we  start,  and  then  could  collect  all  these  various 
substances  formed  by  the  burning  and  in  any  way  measure  their 
mass,  we  should  find  that  this  is  considerably  greater  than  the  mass 
of  wood.  Thus  we  have  not  only  as  much  matter  as  in  the  wood  with 
which  we  started,  but  in  reality  more,  because  some  oxygen  gas  from 
the  air  combined  with  the  wood  as  it  burned.  If  the  mass  of  oxygen 
used  were  also  measured,  we  should  find  the  sum  of  this  and  of  the 
original  mass  of  the  wood  to  be  just  equal  to  the  mass  of  the  sub- 
stances collected  after  the  combustion.  It  would  thus  have  been 
proved  that  the  mass  (amount  of  matter)  is  absolutely  unchanged, 
although  the  form  is  very  different.  Many  experiments  of  this  sort 
have  been  made ;  but  the  most  conclusive  proof  of  the  indestructibil- 
ity of  matter  is  to  be  found  in  the  fact  that  all  over  the  world  chem- 
ists, physicists,  and  artisans,  are  working  upon  processes  which  would 
surely  fail  if  matter  were  not  indestructible. 

The  fact  that  matter  may  change  in  form  in  an  endless 
variety  of  ways,  but  that  the  total  amount  of  matter  does 
not  change,  is  sometimes  called  the  principle  of  the  Con- 
servation of  Matter. 


INERTIA.  65 

Inertia  has  already  been  somewhat  discussed  (pages  30 
to  32).  We  may  explain  it  by  saying  that  a  particle  of  mat- 
ter possesses  absolutely  no  power  to  change  its  velocity  or 
direction  of  motion.  If  the  velocity  and  direction  of  mo- 
tion of  any  material  particle  or  body  does  change,  it  is  be- 
cause of  the  action  of  energy  upon  it.  The  general  law 
which  expresses  the  property  of  inertia  is  Newton's  first  law 
of  motion  (see  page  31).  This  law  is  based  wholly  on  ex- 
periment ;  but  we  find  very  conclusive  evidence  for  it  also 
when  we  consider  what  would  happen  if  a  body  had  power 
to  move  itself.  Such  power  would  involve  a  suspension  of 
the  laws  of  energy,  if  not  an  annihilation  of  energy  itself. 

Start  a  ball  rolling  (without  any  twist  or  spin)  along  a  level  floor, 
or,  better  still,  on  smooth  ice,  and  watch  its  motion.  Notice  first  that 
it  moves  in  a  straight  line.  Unless  it  meets  with  obstacles,  it  does  not 
move  upward,  or  sidewise,  or  backward.  To  think  of  it  as  jumping 
upward,  or  stopping  of  itself  and  moving  backward,  strikes  you  as 
absurd — which  is  only  a  proof  of  the  uniformity  of  your  experience  to 
the  contrary.  The  ball  can  not  move  downward,  because  of  the  floor 
or  ice ;  we  know  that  its  tendency  to  move  downward  is  not  due  to 
itself,  but  is  owing  to  an  action  in  which  the  earth  is  concerned,  and 
that  the  floor  merely  counterbalances  this  action.  The  floor  does  not 
in  any  way  alter  the  motion  of  the  ball.  If  the  earth  were  not  present, 
there  would  be  no  need  of  the  floor.  The  ball,  then,  moves  onward  in 
the  direction  in  which  it  started,  merely  because  nothing  acts  to 
change  that  direction.  It  does  not  of  itself  tend  to  change  the  direc- 
tion of  its  own  motion.  This  is  one  evidence  that  it  is  inert. 

Notice  next  that  the  ball  keeps  on  moving  over  a  long  distance ;  and 
that  the  smoother  the  surface  upon  which  it  rolls,  the  farther  it  will 
move  when  started  with  the  same  speed.  Now  we  know  that  there  are 
two  actions  which  tend  to  stop  it.  These  are  the  resistance  of  friction 
against  the  floor  and  the  resistance  of  the  air.  We  can  diminish  the 
first  by  experimenting  on  a  smoother  surface,  and  make  the  second  less 
effective  by  using  larger  and  larger  balls.  "We  find  as  we  do  so  that 
the  distance  the  ball  will  go  increases,  and  we  may  therefore  infer  that 
if  we  could  entirely  remove  these  resistances  the  ball  would  continue 
to  move  at  the  speed  with  which  it  started,  and  that  it  would  move 
with  uniform  velocity.  The  ball  does  not,  therefore,  of  itself  tend  to 
change  its  speed.  This  is  a  second  evidence  that  it  is  inert. 


66       PROPERTIES  AND  CONSTITUTION  OF  MATTER. 

Take  another  example:  Throw  a  ball  or  stone  horizontally.  It 
does  not  continue  to  move  in  a  straight  line  and  with  the  speed  of 
starting,  but  falls  in  a  curve  toward  the  earth  and  slows  up  in  speed. 
Now,  we  find  by  experiment  that  it  falls  toward  the  earth  just  as  fast 
as  it  would  if  dropped  from  the  hand  and  not  thrown  horizontally. 
Hence  its  curved  motion  is  wholly  due  to  its  falling  toward  the  earth, 
and  this  is  caused  by  the  energy  of  gravitation,  and  is  therefore  not 
due  to  the  body  itself  alone.  Its  slowing  up  in  speed  is  caused  by  the 
resistance  of  the  air.  Hence  we  infer  that,  if  these  two  actions  in 
which  outside  bodies  share  should  be  removed,  the  ball  would  go  on  in 
a  straight  line  with  its  original  velocity. 

Select  for  yourself  and  study  out  other  examples. 

Inertia  may  be  further  illustrated  by  piling  up  half 
a  dozen  books  with  a  smooth-covered  one  at  the  bottom. 
Slide  them  swiftly  across  the  table-top  by  pushing  against 
the  bottom  one.  Place  an  obstruction  in  the  way,  such  as 
the  other  hand  held  firmly  down  against  the  table,  and  let 
the  bottom  book  strike  against  it  suddenly.  What  be- 
comes of  the  top  books  ?  How  is  this  due  to  inertia  ? 

Pile  up  the  books  again.  Push  the  bottom  one  vio- 
lently. What  becomes  of  the  top  ones?  Why? 

Passengers  often  stand  in  the  aisle  of  a  railroad-car  as  it  is  ap- 
proaching the  station.  When  the  car  stops  with  some  suddenness, 
they  plunge  violently  forward  and  sometimes  fall.  Why?  They  gen- 
erally say  that  they  are  "  thrown  "  about  in  such  a  case.  Are  they 
thrown  in  the  sense  that  a  ball  is  thrown  from  the  hand  f  A  railroad 
train  in  motion  will  not  stop  until  it  has  expended  all  its  energy  of 
motion  in  heat  and  other  forms  of  energy  at  the  brakes,  on  the  rails, 
in  the  air,  etc.  This  may  be  said  to  be  due  to  its  inertia. 

All  these  and  similar  examples  should  show  you  how 
energy  depends  upon  inertia ;  but  inertia  is  only  the  prop- 
erty, and  energy  is  the  thing.  Neither  is  due  to  the  other. 

QUESTIONS.— Name  the  Essential  Properties  of  matter.  Why  are  they  properties 
of  matter  rather  than  of  objects  ?  State  some  properties  that  characterize 
bodies  and  not  the  atoms  of  which  they  are  composed.  What  is  Mass  ?  Exten- 
sion ?  What  is  meant  by  Volume  ?  The  dimensions  of  a  body  ?  Have  micro- 
scopic objects  length,  breadth,  and  thickness  ?  Perhaps  your  teacher  or  some 
friend  will  let  you  look  through  a  microscope  at  objects  too  small  to  be  seen 


D 


IVISIBILITY.  67 


with  the  unaided  eye.  Prove  that  a  sheet  of  gold-leaf  has  thickness.  Define 
and  illustrate  Impenetrability.  If  you  fill  a  tumbler  to  the  brim  with  water  and 
drop  in  a  bullet,  what  will  take  place  ?  What  does  this  prove  ?  Show  how  the 
atoms  of  one  body  may  lie  in  the  spaces  between  the  atoms  of  another  body. 
What  do  we  mean  by  the  Indestructibility  of  matter  ?  Illustrate  by  the  evapo- 
ration of  water  from  a  tumbler  ;  by  the  burning  of  wood.  What  has  become  of 
the  matter  contained  in  the  objects  apparently  destroyed  ?  Take  the  case  of 
the  oil  burning  in  your  lamp.  Is  a  particle  of  its  substance  lost  ?  What  be- 
comes of  the  body  after  death  ?  State  the  most  conclusive  proof  that  matter  is 
indestructible.  What  is  meant  by  the  Conservation  of  Matter  ?  Explain  Iner- 
tia. If  a  body  had  power  to  move  itself,  what  would  be  the  effect  on  the  laws  of 
energy  ?  Illustrate  inertia  by  the  case  of  the  ball  rolling  along  a  smooth  floor  ; 
by  the  case  of  the  ball  thrown  horizontally  ;  by  the  case  of  the  books  pushed 
along  the  table.  Did  you  ever  notice  the  effect  of  inertia  when  a  train  was  en- 
tering the  depot  or  a  ferry-boat  landing  in  its  slip  ?  Why  is  it  dangerous,  when 
the  horses  are  running,  to  jump  from  a  carriage  ?  Because  the  feet  cease  to 
move  the  instant  they  strike  the  ground,  while  the  inertia  of  the  body  carries 
it  forward.  On  what  principle  is  the  snow  shaken  from  your  arctics  by  kick- 
ing against  the  door-post  ?  Can  you  think  of  other  ways  in  which  \ve  avail 
ourselves  of  inertia  ? 


CONSTITUTION  OF  MATTER. 

Divisibility. — Any  object  may  be  cut  or  broken  into 
pieces  and  these  pieces  may  be  made  into  others  still  smaller. 
This  process  of  mechanical  subdivision  may  be  kept  up  un- 
til the  substance  is  reduced  to  a  powder,  the  limit  being  ap- 
parently only  the  lack  of  suitable  means  of  making  it  finer. 
By  hammering  thin  sheets  of  gold  repeatedly  between  sheets 
of  animal  membrane,  the  gold-beater  can  reduce  them  to  a 
thickness  of  only  three  million ths  of  an  inch.  By  an  in- 
genious process,  a  film  of  gold  has  been  produced  of  a 
thickness  estimated  at  one  quarter  of  a  millionth  of  an 
inch.  The  average  diameter  of  the  water-drops  in  a  cloud 
causing  the  halo  which  you  have  often  seen  around  the  sun 
or  moon  is  calculated  to  be  one  thirteen  thousandth  of  an 
inch.  Such  was  probably  about  the  size  of  the  dust-parti- 
cles in  the  air  which  produced  the  remarkable  sunset  colors  so 
noticeable  in  1883-'84  after  the  Krakatoa  eruption.  Soap, 
bubbles,  just  before  breaking,  may  be  as  thin  as  one  fortieth 
of  the  millionth  of  an  inch ;  and  it  has  been  computed  that 
a  half-pound  of  spider's  web  would  encircle  the  earth. 


68  CONSTITUTION  OF  MATTER. 

All  these  facts  go  to  show  that  matter  can  be  divided 
into  parts  of  extreme  smallness  or  layers  of  extreme  thin- 
ness, which  is  practically  the  same  thing.  This  property  is 
called  Divisibility.  But  is  the  divisibility  infinite?  Can 
matter  be  subdivided  indefinitely  if  suitable  mechanical 
means  can  be  provided  ?  Or  should  we  eventually  come  to 
a  piece  which  could  not  be  reduced  to  any  smaller  parts  ? 
If  the  latter  be  true,  then  matter  is  not  infinitely  divisible, 
but  is  "  granular  "  in  structure — that  is,  it  is  built  up  of 
separate  individual  parts.  If  matter  is  perfectly  continu- 
ous, we  can  not  explain  the  properties  of  compressibility 
and  elasticity  (see  page  50).  If  it  is  granular,  we  can  ex- 
plain these  properties,  as  well  as  many  others,  by  assuming 
that  the  grains  or  ultimate  particles  are  not  in  contact 
throughout  the  substance,  but  are  separated  by  intervals. 

There  is  a  very  wide  range  of  chemical  as  well  as  physical  facts 
which  seem  to  require  the  hypothesis  that  our  recognized  kinds  of 
matter  are  built  up  of  parts  or  units  called  Atoms,  each  of  which  is  of 
fixed  mass.  Many  of  these  facts  require  that  the  atoms  should  be  as- 
sumed, not  to  be  in  contact  with  one  another,  but  at  a  distance  apart 
which  is  generally  greater  than  their  own  diameters.  They  also  involve 
the  assumption  that  these  atoms  are  in  to-and-fro  motion  and  in  rota- 
tion. The  facts  do  not,  however,  require  that  the  space  separating  the 
atoms  should  be  empty,  but  admit  of  its  being  filled  with  a  material 
offering  no  resistance  to  the  motion  of  the  atoms  through  it. 

A  hypothesis  has  been  recently  proposed  (by  Sir  William  Thomson 
in  1862)  which  seems  to  fulfill  these  conditions.  It  assumes  that  the 
atoms  are  rotating  rings  or  vortexes  of  some  given  material.  You  have 
doubtless  seen  the  rings  of  smoke  sent  up  from  the  stack  of  a  locomo- 
tive, and  have  noticed  that  the  smoke  composing  these  rings  is  always 
in  rotation.  If  you  follow  the  motion  of  any  individual  part  of  the  smoke 
at  a  section  of  the  ring,  you  will  see  that  it  moves  upward  on  the  inside 
of  the  ring,  out  over  the  top,  down  the  outside,  inward  at  the  bottom, 
and  again  upward  as  before,  thus  whirling  around  in  a  circle  in  a  ver- 
tical plane.  A  ring  also  frequently  rotates  as  a  whole  around  its  axis. 
It  is,  moreover,  often  in  vibration. 

With  an  apparatus  like  the  one  pictured  in  Pig.  19,  you  can  form 
and  study  such  rings.  Make  a  box  of  pasteboard  or  wood,  about  8 
inches  broad  by  8  inches  high  by  18  inches  long,  leaving  both  ends 


THOMSON'S  HYPOTHESIS. 


69 


open.  Over  one  end  of  it  stretch  loosely  a  piece  of  cloth  and  cover 
the  other  end  with  a  cardboard  in  which  is  cut  a  circular  hole  of  four 
inches  or  more  in  diameter.  Inside  the  box  place  a  dish  of  strong 
ammonia  and  another  of  strong  hydrochloric  acid,  the  fumes  of  which 


FIG.  19.— VORTEX  RINGS,  ILLUSTRATING  THOMSON'S  HYPOTHESIS. 


will  mix  and  form  within  the  box  a  white  cloud  of  smoke  consisting 
of  particles  of  ammonium  chloride.  Strike  the  cloth  end  of  the  box  a 
tap  with  the  hand.  A  puff  of  this  smoke  will  come  out  at  the  open 
end  and  move  slowly  onward.  Notice  that  it  has  the  form  of  a  ring 
whose  particles  are  revolving  just  as  in  the  smoke-rings  from  the  loco- 
motive. Tap  again  and  send  out  another,  then  a  third,  and  so  on.  By 
regulating  the  energy  of  the  blows,  you  can  make  the  rings  move  faster 
or  more  slowly,  and  can  thus  cause  them  to  collide,  move  through  one 
another,  etc.  Notice  how  they  rebound  on  collision  with  each  other, 
as  if  elastic,  and  how  they  change  form  on  striking  solid  surfaces. 
They  finally  break  up  and  are  brought  to  rest,  owing  to  the  friction  of 
the  air,  for  they  are  really  air-rings  revolving  in  air,  but  made  visible 
by  the  smoke.  Such  rings  are  called  vortex-rings. 

Thomson's  hypothesis  assumes  that  atoms  are  merely  such  vortex- 
rings  existing  in  a  homogeneous  continuous  material  and  consisting 
of  it.  These  atoms  are  supposed  to  differ  in  many  respects,  especially 
in  size,  rate  of  rotation,  and  in  the  kind  anjl  amount  of  vibration  which 
they  possess,  such  differences  being  sufficient  to  account  for  the  varie- 
ties of  atoms  or  of  matter  which  we  recognize.  The  material  is  of  such 
a  nature  as  to  have  no  friction  between  its  parts,  so  that  the  vortex- 


YO  CONSTITUTION  OF  MATTER. 

rings,  once  started,  must  continue  forever  and  without  change  of  char- 
acter. It  has  been  found  possible  to  explain  upon  this  hypothesis  some 
of  the  fundamental  properties  and  phenomena  of  matter. 

Atomic  Theory. — Atoms. — We  are  not  obliged,  for 
present  purposes,  to  discuss  the  questions  just  suggested. 
Little  is  settled  in  regard  to  them,  and  the  hypotheses  ad- 
vanced are  very  incomplete.  We  will,  therefore,  concern 
ourselves  only  with  those  few  hypotheses  which  it  is  con- 
venient to  use  as  we  proceed. 

Let  us  assume — 

I.  That  material  bodies  are  built  up  of  extremely  minute 
particles  of  matter  which  are  called  Atoms. 

II.  That  these  atoms  are  not  divisible — that  is,  that  they 
are  the  smallest  parts  which  can  exist. 

III.  That  every  atom  is  indestructible  and  unchange- 
able. 

IV.  That  atoms  are  of  several  kinds,  each  possessing  its 
own  characteristics ;  but  that  the  number  of  kinds  is  lim- 
ited, being,  as  far  as  is  now  known,  about  seventy. 

V.  That  there  are  certain  essential  properties  common 
to  all  atoms,  and  thus  to  all  matter. 

These  assumptions  are  a  somewhat  incomplete  statement  of  the 
hypotheses  which  form  the  basis  of  the  so-called  "  Atomic  Theory  "  of 
the  constitution  of  matter.  The  complete  theory  embraces  other  hy- 
potheses and  offers  explanations  of  many  laws  and  phenomena.  There 
are  serious  objections  to  it,  and  it  is  to  be  regarded  only  as  a  good 
working  hypothesis  on  a  very  difficult  subject. 

Chemical  Energy  and  Affinity. — The  atoms  of  the 
different  kinds  of  matter  (elements)  show  a  tendency  to 
unite  with  one  another  and  form  compound  substances. 
This  tendency  to  combination  is  stronger  between  some 
kinds  of  atoms  than  others,  and  varies  with  temperature, 
pressure,  and  other  physical  conditions.  It  follows  certain 
remarkable  laws,  which  are  explained  in  the  study  of  chem- 
istry, and  is  due  to  a  form  of  energy  called  Chemical  En- 


ATOMIC   THEORY.  71 

ergy,  regarding  whose  exact  nature  little  is  known.  The 
forces  produced  by  the  action  of  chemical  energy  are  called 
chemical  forces  or,  more  generally,  Chemical  Affinity.  They 
are  tendencies  to  acceleration  among  the  atoms. 

Molecules  as  distinguished  from  Atoms. — When, 
under  the  influence  of  chemical  energy,  the  atoms  of  ele- 
ments unite  to  form  compounds,  they  appear  to  combine 
only  into  small  groups  containing  a  few  atoms  each.  Such 
groups  constitute  Molecules.  A  molecule,  then,  is  a  group 
of  atoms  bound  together  by  chemical  energy.  Thus,  a  mole- 
cule of  water  consists  apparently  of  two  atoms  of  hydrogen 
united  with  one  of  oxygen.  It  is  evident,  therefore,  that  if 
the  molecules  of  a  compound  substance  were  to  be  broken 
up,  the  character  of  the  compound  would  disappear. 

Chemical  study  leads  us  to  believe,  that,  with  few  exceptions, 
atoms  do  not  exist  separately — that  is,  uncombined  with  other  atoms — 
even  in  elementary  substances.  For  instance,  when  hydrogen  gas  (an 
elementary  substance)  exists  uncombined,  its  molecules  are  not  single 
atoms,  but  consist  of  two  atoms  united  by  their  chemical  energy. 

We  may,  therefore,  define  the  Molecule  of  any  substance 
as  the  smallest  portion  of  that  substance  which  exists  ~by  it- 
self, and  the  Atom  as  the  smallest  portion  of  any  element 
which  exists  even  in  combination.  Thus  any  atom  is  of  one 
kind  of  matter  throughout. 

The  molecule  of  zinc,  cadmium,  mercury,  and  possibly  of  some 
few  other  elements,  seems  to  contain  only  one  atom.  The  molecule  of 
most  elements  contains  two  atoms  ;  that  of  phosphorus  and  of  arsenic, 
four.  The  molecules  of  compounds  contain  different  numbers  of 
atoms,  according  to  the  complexity  of  the  substances — sometimes  as 
many  as  several  hundred.  It  is  probable  that  the  molecules  of  gases 
are  separate  from  one  another ;  while  those  of  liquids  are  somewhat 
tangled  together  into  groups  or  bunches,  and  those  of  solids  are 
crowded  still  more  closely. 

Spaces  between  Molecules  or  Atoms. — Atoms  and 
molecules  are  supposed  not  to  be  in  actual  contact  with  one 


72  CONSTITUTION  OF  MATTER. 

another,  but  to  be  separated  by  distances  which  are  usually 
great  as  compared  with  the  size  of  the  particles  themselves. 
Thus  the  apparent  volume  of  a  body  is  much  larger  than 
that  which  the  molecules  or  atoms  would  occupy  if  packed 
solidly  together.  The  latter  appear  to  be  kept  apart,  not  by 
reason  of  any  repulsion  between  them,  but  because  they  are 
in  continuous  to-and-fro  motion. 

Perhaps  you  can  form  an  idea  of  how  this  can  be  by  imagining  a 
number  of  boys  packed  so  closely  together  that  there  is  no  room  to  crowd 
in  another.  They  would  occupy  a  certain  space  on  the  ground.  Now, 
let  every  boy  try  to  move  to  and  fro,  each  in  a  different  direction,  aim- 
ing to  move  back  and  forth  through  just  one  full  step  and  no  more,  and 
let  him  change  the  direction  at  each  step.  With  the  exception  of  those 
on  the  edges,  the  boys  will  hardly  be  able  to  move  at  first ;  but  those 
next  the  edges  will  gradually  push  out  their  fellows ;  these  in  turn 
will  be  pushed  out  by  those  farther  in,  and  so  on.  The  result  you  can 
easily  foresee,  and  if  you  try  the  experiment  you  will  find  that  the 
crowd  gradually  spreads  over  more  space  until  each  boy  has  the  room 
he  needs  to  move  in.  The  jostling  to  and  fro  forces  the  boys  apart 
and  keeps  them  apart.  You  can  see  also  that  it  would  continue  to  keep 
them  apart  even  if  each  boy  had  a  slight  tendency  to  move  toward 
the  center  of  the  crowd  rather  than  to  remain  where  he  was  placed. 

Thus  the  molecules  of  a  solid  substance  are  held  apart  from  one 
another  merely  because  they  have  a  to-and-fro  motion  which  they  must 
keep  up.  The  molecules  are  supposed  to  be  like  elastic  balls,  so  that 
when  they  strike  one  another  they  bound  off  without  loss  of  energy. 

Porosity. — Fill  a  tumbler  with  shot,  as  in  Fig.  20. 
Notice  that  the  shot  are  separated  by  spaces  or  interstices ; 
they  do  not  fill  the  tumbler  full.  Imagine  the  shot  to  rep- 
resent the  molecules  of  a  substance ;  then  the  spaces  repre- 
sent what  are  called  the  pores  of  the  substance,  and  the 
property  of  having  these  pores  is  called  Porosity.  But  the 
shot  do  not  represent  these  pores  properly,  for,  as  just  ex- 
plained, the  molecules  are  supposed  not  to  be  in  contact  as 
the  shot  are,  but  much  farther  apart.  Hence  the  pores  are 
much  larger  in  proportion  to  the  molecules  than  the  spaces 
between  the  shot  are  in  proportion  to  the  shot.  Let  us  ex- 
amine some  proofs  that  such  pores  exist. 


POROSITY.  73 

Take  a  glass  tube  bent  into  the  form  shown  in  No.  13  of  the  col- 
lection of  apparatus  on  page  173.    The  short  arm  of  this  tube  is  closed 
at  the  top,  the  long  arm  is  open.     Pour  a  little  mercury  into  the  long 
arm.     It  will  fall  to  the  bottom  and  in- 
close above  it  some  air  in  the  short  arm. 
Pour  in  more  mercury,  and  the  volume 
of  this  air  will  be  lessened.    Pour  in 
additional  mercury,  and  you  will  find 
that  the  air  is  gradually  reduced  to 
smaller  and  smaller  volume.    We  are 
then  compressing  the  air — that  is,  forc- 
ing the  same  mass  to  occupy  less  space, 
or  making  the  air  more  dense.     Now, 
the  only  way  in  which  we  can  picture 
this   action  to  ourselves,  if  we  regard 
matter  to  be  impenetrable,  seems  to  be       FJG  20._TuMBLER  OP  SHOT. 
by  imagining  the  air  to  consist  of  par- 
ticles or  molecules  with  spaces  between  them,  and  inferring  that  when 
the  air  is  compressed  the  molecules  are  simply  brought  nearer  to  one 
another.    Solids  and  liquids  are  also  compressible,  but  much  less  so  than 
gases.     Compressibility,  then,  seems  to  indicate  that  matter  is  porous. 

It  has  been  stated  (page  63)  that  water  vapor  at  ordinary 
temperatures  occupies  about  60,000  times  as  much  space  as 
the  same  mass  of  liquid  water  occupies.  To  understand 
this  we  must  imagine  the  water  as  made  up  of  molecules 
with  spaces  between  them,  which  are  much  larger  in  the 
condition  of  vapor  than  in  that  of  liquid.  Thus  the  mole- 
cules of  the  vapor  appear  to  be  about  forty  times  as  far 
apart  on  the  average  as  those  of  the  liquid  water. 

Mix  thoroughly  together  two  exactly  equal  volumes  of  alcohol  and 
water.  The  mixture  might  be  expected  to  have  just  double  the  vol- 
ume of  either  separately — that  is,  the  sum  of  the  separate  volumes ; 
but  this  will  not  be  the  case.  The  volume  of  the  mixture  will  be  about 
six  per  cent  less  than  the  sum  of  the  two.  This  experiment  may  be 
made  by  filling  a  small  flask  with  water,  and  then  removing  exactly 
one  half  of  the  water  and  replacing  it  with  alcohol.  The  resulting 
liquid  stands  much  lower  than  before  in  the  neck  of  the  flask.  There 
are  other  liquids  which  show  the  same  action. 

Fill  a  tumbler  with  water.     Put  in  a  pinch  of  salt.     After  a  few 


74  CONSTITUTION  OF  MATTER. 

minutes,  water  taken  from  any  part  of  the  tumbler  will  taste  salt.  The 
salt  has  been  dissolved,  as  we  say,  by  the  water.  How  do  we  account 
for  this  ?  We  suppose  that  the  salt  has  become  distributed  through 
the  pores  of  the  liquid,  or  that  the  molecules  of  salt  have  passed  off 
into  and  through  the  spaces  between  the  molecules  of  the  water  and 
have  thus  become  distributed  into  all  parts  of  it.  Sugar,  blue  vitriol, 
and  a  multitude  of  familiar  solids,  thus  dissolve  in  water,  as  do  also 
gases.  The  effervescence  of  soda-water  is  due  to  the  bubbling  out  of 
carbonic-acid  gas,  which  was  held  in  solution  under  pressure  but  is 
given  out  when  the  pressure  is  removed. 

In  many  cases  of  solution,  the  volume  of  the  liquid  after  solution 
is  less  than  its  original  volume  plus  that  of  the  solid  added. 

Into  the  tumblerful  of  shot  pour  water,  or  finer  shot,  or  sand, 
shaking  it  well.  You  can  thus  put  a  considerably  greater  mass  into 
the  tumbler,  which  has  already  as  many  of  the  original  shot  as  it  can 
hold.  If  these  shot,  instead  of  being  in  contact,  were  in  some  way  held 
farther  apart  as  the  molecules  seem  to  be,  you  could  put  still  more 
material  into  the  pores.  The  shot  thus  illustrate  the  porosity  of  mat- 
ter, but  only  in  a  crude  way,  for  the  fact  that  the  molecules  are  in  mo- 
tion and  the  shot  are  at  rest  makes  a  great  difference  in  the  conditions. 
Moreover,  the  molecules  should  not  be  imagined  to  be  hard,  spherical 
bodies.  They  are  almost  certainly  not  so,  and  we  have  no  idea  what 
they  are  like.  Indeed,  we  can  not  be  too  careful  to  remember  that  all 
our  notions  about  molecules  are  merely  hypotheses. 

Besides  the  Molecular  Pores  just  described,  bodies 
have  cavities  of  sensible  size  which  are  often  called  pores. 
Thus,  a  sponge,  a  loaf  of  bread,  a  brick,  wood,  the  majority 
of  substances,  even  gold  and  granite,  are  full  of  such  holes, 
and  are  therefore  called  porous.  This  is  illustrated  in  the 
familiar  process  of  filtering  or  straining.  It  is  well,  there- 
fore, to  bear  in  mind  that  there  are  two  classes  of  pores,  and 
to  call  the  molecular  spaces  molecular  pores,  or,  better,  in- 
termolecular  (between  the  molecules). 

Size  of  Atoms  and  Molecules. — There  are  phenom- 
ena which  enable  physicists  to  obtain  an  approximate  idea 
of  the  number  of  molecules  ordinarily  contained  in  given 
volumes  of  certain  substances,  and  even  some  notion  as  to 
the  probable  size  of  the  molecules  themselves.  Imagine  a 


SIZE  OF  ATOMS  AND  MOLECULES.  Y5 

cube  of  water  one  inch  on  a  side  magnified  until  the  length 
of  its  side  is  equal  to  the  diameter  of  the  earth.  Then  in 
this  enormously  magnified  cube  there  would  be  one  molecule 
to  every  cubic  inch,  and  of  this  space  the  actual  molecule 
itself  would  probably  occupy  about  one  twentieth.  Another 
way  of  stating  the  size  is  to  say  that  if  a  drop  of  water  were 
magnified  to  the  size  of  the  earth,  the  molecules  would  oc- 
cupy spaces  greater  than  those  filled  by  small  shot,  and  less 
than  those  occupied  by  base-balls.  Of  these  spaces  the  mol- 
ecules would  occupy  about  one  twentieth,  as  before. 

The  smallest  object  which  would  fee  visible  under  the  most  power- 
ful microscope  is  probably  not  smaller  than  a  cube  of  one  one  hun- 
dred-thousandth of  an  inch  on  a  side.  Such  a  cube  would  contain 
from  60,000,000  to  100,000,000  molecules  of  oxygen  or  of  nitrogen. 
This  would  mean  twice  as  many  atoms,  as  each  molecule  of  these  gases 
contains  two  atoms.  Now,  as  the  molecules  themselves  fill  but  perhaps 
one  twentieth  of  this  space,  it  is  easy  to-  understand  that  a  single 
molecule  is  much  too  small  to  be  seen  even  with  the  most  powerful 
magnification  which  we  can  at  present,  or  perhaps  ever,  produce. 

QUESTIONS. — Explain  Divisibility.  Give  some  illustrations  of  the  extreme  thinness 
to  which  layers  of  certain  substances  can  be  reduced  ;  of  the  extreme  smallness 
of  certain  particles  in  the  air.  Is  matter  infinitely  divisible  ?  What  do  many 
chemical  and  physical  facts  require  for  their  explanation  ?  What  do  they  in- 
volve as  regards  motion  among  the  atoms  ?  Are  the  spaces  separating  the 
atoms  necessarily  empty  ?  State  Thomson's  hypothesis.  Show  how  it  may  be 
illustrated  with  vortex-rings.  How  are  the  atoms  supposed  to  differ,  and  to 
what  do  these  differences  give  rise  ?  State  the  five  hypotheses  that  form  the 
basis  of  the  so-called  Atomic  Theory.  What  are  elements  ? 

Describe  Chemical  Energy  ;  Chemical  Affinity.  What  is  chemistry  ?  Discrimi- 
nate carefully,  with  illustrations,  between  molecules  and  atoms.  Do  atoms  ex- 
ist uncombined  with  other  atoms  ?  How  is  it  in  the  case  of  elementary  sub- 
stances ?  Instance  molecules  that  contain  one  atom  ;  two  atoms  ;  four  atoms. 
Compare  the  molecules  of  gases,  liquids,  and  solids,  as  regards  separation. 
Explain  and  illustrate  the  principle  on  which  atoms  and  molecules  are  kept 
apart.  What  is  Porosity  ?  Can  you  mention  any  substance  which  has  visible 
pores  ?  Distinguish  between  these  and  molecular  pores.  What  is  the  result 
of  mixing  equal  volumes  of  alcohol  and  water  ?  Of  mixing  salt  and  water  ? 
How  does  the  volume  of  the  liquid  of  the  solution  often  compare  with  the 
original  volume  plus  that  of  the  solid  ? 

[f  two  volumes  of  hydrogen  were  mixed  with  one  of  oxygen  and  exploded,  the 
substance  produced  would  be  water.  If  the  explosion  were  made  over  mercury 
in  such  a  way  that  the  water  could  be  collected,  it  would  be  found  that  the 
amount  of  water  from  a  litreXsee  page  540)  of  the  gases  would  be  but  a  few 


76  MASS,  FORCE,  ENERGY,  AND  WORK. 

drops.  How  does  this  illustrate  porosity  ?  How  is  the  foam  on  a  glass  of  soda- 
water  due  to  this  same  property  of  matter  ?  How  may  the  mass  in  a  tumbler 
filled  with  buckshot  be  increased  ?  Why  ?  Would  a  tumbler  filled  with  melted 
lead  be  more  massive  than  if  filled  with  shot  ?  What  does  the  familiar  pro- 
cess of  filtering  or  straining  liquids  prove  ?  Express  your  idea  of  the  extreme 
minuteness  of  molecules  and  atoms. 


MEASUREMENT  OF   MASS,    FORCE, 
ENERGY,    AND  WORK.        '  • - 

MASS  MEASUREMENT. 

Equal  Masses. — In  the  arrangement  of  a  system  of 
measurement  of  mass,  force,  energy,  etc.,  we  must  begin 
with  a  definition  of  what  constitutes  equal  masses.  Two 
masses  are  said  to  be  equal  when  the  same  force,  acting  upon 
them  separately,  will  produce  in  them  equal  accelerations. 

We  have,  then,  first  to  show  some  way  by  which  we  can 
actually  measure  off  equal  masses,  in  accordance  with  this 
definition ;  secondly,  to  explain  how  we  can  produce  graded 
sets  of  masses  (usually  called  sets  of  weights) ;  and,  thirdly, 
to  state  the  units  of  mass  generally  employed.  How  masses 
are  actually  measured  in  practice  by  the  process  called  weigh- 
ing will  be  described  in  the  section  on  forces,  as  it  is  done 
by  using  of  the  force  of  weight. 

First,  then,  how  can  we  apply  exactly  the  same  force  to 
make  it  act  on  different  portions  of  matter  in  such  a  way  that 
we  can  measure  the  accelerations  produced  ?  Weight  affords 
us  the  easiest  means  of  doing  so ;  for  we  may  assume  that 

NOTE.— Hereafter  we  shall  speak  of  acceleration,  change  of  direction  of  mo- 
tion, distortion  of  bodies  by  stretching  or  bending,  etc.,  as  produced  by  the  action 
of  force,  just  as  if  force,  and  not  the  energy  producing  it,  were  the  real  cause. 
This  is  more  convenient,  and  is  almost  universally  employed,  but  the  pupil  will 
find  himself  freed  from  much  confusion  of  thought  if  he  will  always  bear  in  mind 
that  the  real  cause  is  in  all  cases  energy,  and  that  force  is  never  anything  but  a 
condition  of  matter  incidental  to  the  action  of  energy. 


MASS  MEASUREMENT. 


experience  has  shown  us  that  the  weight  of  a  given  body  at 
the  same  part  of  the  earth's  surface  is  constant,  unless  some 
matter  is  either  added  to  or  taken  away  from  the  body. 

Obtain  a  board  (A  B,  Fig.  21)  8  feet  or  more  long,  9  to  12  inches 
wide,  and  \\  to  2  inches  thick.  One  surface  must  be  very  smooth,  and 
must  always  be  a  perfect  plane.  Mark  across  the  board  black  lines,  one 
eighth  of  an 
inch  wide,  at 
equal  intervals 
of  10  inches 
throughout  its 
length.  Con- 
struct a  strong 
cart  about  10 
inches  long  by 
6  inches  broad. 
Its  wheels  may 
be  of  wood, 
and  about  4 

inches  in  diam-        FIG.  21.— LOADED  WAGON,  WITH  PULLEY  AND  SCALE  PAN. 
eter ;  but  brass 

or  iron  is  preferable.  They  must  be  carefully  turned  in  a  lathe  into 
true  circles.  The  axles  must  be  of  brass  or  iron,  and  the  wheels  well 
centered.  At  one  end  of  the  board  A  B  fasten  a  grooved  pulley  D,  4 
or  5  inches  in  diameter.  This  must  also  turn  very  freely,  and  its  top 
at  D  should  be  at  the  same  height  above  the  board  as  the  point 
of  attachment  to  the  cart.  A  cord  is  run  from  E  over  D  to  a 
strong  pan  W.  The  board  must  be  laid  horizontally  on  a  table,  or 
on  brackets  6  feet  or  more  above  the  floor,  to  give  room  for  the 
descent  of  W. 

We  are  to  observe  the  accelerations  produced  in  the  loaded  cart  by 
a  weight  at  W.  To  do  this  properly,  it  is  necessary  that  all  resistances, 
of  which  friction  is  the  chief,  should  be  reduced  as  much  as  possible.  Oi\ 
the  axles.  Then  remove  the  cord  and  pan  by  unhooking  at  E.  Give 
the  cart  a  gentle  push  toward  D.  It  will  roll  a  short  distance,  and  then 
stop  because  of  friction.  Raise  the  end  A  of  the  board  considerably, 
and  push  again.  The  cart  will  roll  down  the  board  with  accelerated 
motion.  Now  lower  A  gradually,  pushing  the  cart  from  time  to  time. 
By  repeated  trials  a  height  will  be  found  for  A  which  will  just  keep 
the  cart  in  very  slow  motion  when  started,  and  will  not  increase  its 
speed.  Leave  the  board  in  this  position,  for  here  the  weight  of  the 


78  MASS,  FORCE,  ENERGY,  AND  WORK. 

cart  just  about  neutralizes  the  resistance  of  friction,  and  that  source 
of  error  is  almost  removed. 

Now  hook  the  cord  on  at  E,  and  hang  it  over  D.  Put  into  the  car 
some  sand  or  shot,  and  a  small  amount  of  the  same  into  the  pan.  We 
shall  then  have  a  force  at  W  equal  to  the  sum  of  the  weights  of  the 
sand  and  pan  (we  may  neglect  that  of  the  cord).  This  force  will  be  al- 
ways the  same  so  long  as  no  more  sand  is  put  in  and  none  taken  out. 
We  have,  therefore,  a  constant  force  which  we  will  call  W,  and  which 
tends  to  set  in  motion  all  the  movable  mass,  viz.,  itself  plus  the  mass 
of  the  cart  and  load. 

Some  device  is  needed  to  stop  the  cart  when  in  rapid  motion.  Tie 
up  in  a  bag  two  or  three  pounds  of  sand  or  shot.  Fasten  to  this  a 
strong  cord  about  two  feet  shorter  than  the  board,  and  tie  the  cord 
to  the  rear  end  of  the  cart.  Place  the  sand-bag  upon  the  board  at 
the  end  away  from  the  pulley,  and  leave  the  cord  loosely  coiled  or 
folded  back  and  forth  on  the  board.  Place  also  a  box  or  other  shelf 
at  such  a  distance  below  the  pan  W  that  the  pan  will  rest  upon  it  when 
the  cart  is  two  feet  or  less  from  D.  If,  then,  the  cart  starts  from  the 
rear  end  of  the  board,  it  will  move  along  freely  till  it  reaches  a  point 
where  E  is  one  or  two  feet  from  D.  Then  W  will  cease  pulling,  be- 
cause resting  on  the  shelf,  and  the  sand-bag  will  begin  to  act  as  a  drag 
or  brake  to  stop  the  cart.  If  a  few  inches  of  rubber  tubing  or  coiled 
steel  or  brass  spring  be  put  in  between  the  cart  and  sand-bag,  the  cart 
will  be  less  violently  jerked. 

For  class  illustration,  upright  rods  may  be  inserted  at  the  black 
lines  on  the  board,  and  an  upright  pointer  attached  to  the  cart. 

The  Motion  produced  by  the  Constant  Force  is 
accelerated. — Let  us  now  see  what  the  character  of  the 
motion  is  when  the  constant  force  W  is  moving  the  mass  of 
the  loaded  cart  and  itself.  Pull  the  cart  hack  till  the  point- 
er stands  at  a  line  near  the  starting  end  of  A  B.  Let  it  go, 
and  observe  its  motion.  You  will  see  that  it  moves  slowly 
at  first,  and  then  continually  faster  and  faster — that  is,  the 
motion  is  accelerated.  To  perceive  this  clearly,  count  as 
follows :  At  the  instant  of  releasing  the  cart,  say  zero ;  at 
the  instant  it  crosses  the  next  line  (having  passed  over  one 
space  on  the  board),  count  one;  at  the  third  line,  count 
two ;  and  so  on.  You  will  perceive  in  this  way  that  each 
space  is  passed  over  in  a  less  time  than  the  preceding  one, 


MEASUREMENT   OF  MASSES.  79 

and  that  the  motion  is  thus  accelerated.  If  the  friction  were 
constant,  and  you  had  means  of  observing  accurately,  you 
would  find  that  the  motion  was  uniformly  accelerated. 

The  Bate  of  Acceleration  by  the  same  Force  is 
less  as  the  Mass  moved  is  greater. — Take  out  some  of 
the  sand  from  the  cart,  and  repeat  the  experiment.  The 
cart  will  be  found  to  move  faster.  If  more  load  is  put  in, 
it  will  move  more  slowly.  Thus,  if  we  lessen  the  mass,  the 
same  force  produces  a  greater  acceleration ;  if  we  increase 
the  mass,  it  produces  a  less  acceleration. 

To  measure  the  rate  of  acceleration,  which  is  desirable  for  some 
later  experiments,  make  a  pendulum  by  hanging  any  heavy  body  with 
a  cord  from  any  firm  support,  as  in  No.  9,  page  60.  The  shorter  the 
string,  the  faster  the  pendulum  will  swing.  The  time  occupied  by  the 
cart  in  passing  from  a  mark  near  the  end  A  of 'the  board  to  one  near 
the  end  B  can  be  observed  by  noting  the  number  of  swings  of  the  pen- 
dulum. This  can  be  best  done  by  varying  the  length  of  the  pendulum 
until  it  makes  some  whole  number  of  swings  while  the  cart  is  passing 
from  A  to  B.  By  the  laws  of  uniformly  accelerated  motion,  the  cart 
is  equally  accelerated  when  it  passes  over  the  space  A  B  in  equal  times. 
If  the  cart  passes  from  A  to  B  in  half  a  given  portion  of  time,  the  ac- 
celeration will  be  four  times  as  great  (see  page  20).  If  it  travels  in  one 
third  the  time,  the  acceleration  will  be  nine  times  as  great ;  and  so  on. 

To  measure  off  Equal  Masses  of  the  same  or  of 
Different  Kinds  of  Matter. — Leaving  W  unchanged,  re- 
move all  the  sand  from  the  cart,  and  lay  it  carefully  aside  to 
be  weighed  in  the  next  experiment.  Put  in  its  place  some 
other  kind  of  matter,  for  example,  shot.  The  cart  will  now 
move  faster  or  more  slowly  than  with  the  sand  in  the  last 
experiment,  showing  that  the  whole  mass  moved  is  either 
less  or  greater  than  before. 

By  adding  or  removing  shot,  a  quantity  will  at  length  be  found 
with  which  the  cart  will  move  from  A  to  B  in  exactly  the  same  time  as 
with  the  sand.  Hence  the  rate  of  acceleration  is  the  same — the  same 
force  (weight  of  W)  is  producing  the  same  acceleration  on  two  differ- 
ent collections  of  matter.  We  have,  therefore,  two  masses,  viz.  (cart  4- 
sand  +  mass  at  W)  in  one  case,  and  (cart  +  shot  +  mass  at  W)  in  the 


80  MASS,   FORCE,   ENERGY,  AND  WORK. 

other,  on  which  the  same  force  produces  equal  accelerations.     There- 
fore, these  two  masses  are  equal. 

Further,  as  the  mass  of  the  cart  and  of  W  are  the  same  in  both 
cases,  the  mass  of  the  shot  must  be  equal  to  the  mass  of  the  sand. 
Thus  we  have  a  means  of  determining  by  a  simple  experiment  whether 
two  masses  are  equal,  as  well  as  of  constructing  equal  masses. 

The  Weights  of  Equal  Masses  stretch  a  spring  by 
equal  amounts,  or  counterpoise  each  other  on  a  balance. 

Put  the  sand  of  the  last  experiment  upon  a  spring-balance.  The 
spring  will  be  stretched  by  a  certain  amount.  Replace  the  sand  by  the 
shot,  and  the  spring  will  be  equally  stretched.  The  same  result  will  be 
reached  whatever  kind  of  matter  the  equal  masses  are  composed  of, 
and  however  massive  they  may  be.* 

Instead  of  using  a  spring-balance,  the  sand  and  shot  might  be  put 
in  opposite  pans  of  an  equal-arm  balance,  and  would  then  be  found  to 
counterpoise  each  other. 

The  last  two  experiments  can  be  made  more  satisfactory,  although 
really  no  more  accurate,  by  reversing  their  order.  To  do  so,  measure 
off  by  the  spring-balance  quantities  of  sand  and  shot  which  will  stretch 
the  spring  equally.  Put  the  sand  into  the  cart  and  time  its  passage 
from  A  to  B,  using  a  suitable  weight  at  W.  Replace  the  sand  by  the 
shot,  and  time  again.  The  time  will  be  found  the  same.  This  proves 
that  masses  whose  weights  stretch  the  spring  equally  are  equal  masses, 
As  this  would  be  found  true,  however  massive  the  equal  portions  and 
of  whatever  kind  of  matter,  the  converse  proposition  that  equal  masses 
stretch  the  same  spring  equally  would  be  proved. 

Graded  Sets  of  Masses. — The  principle  just  explained 
enables  us  to  construct  a  graded  set  of  standard  masses.  If 
we  take  the  sand  of  the  foregoing  experiment,  or  any  mass 
of  any  substance,  and  divide  it  into  two  portions  which 
stretch  a  spring  equally  or  which  counterpoise  on  an  equal- 
arm  balance,  the  mass  of  each  portion  must  be  just  half  that 
of  the  original  mass.  Similarly  we  may  divide  the  original 
mass  or  its  parts  into  any  desired  number — 3,  5,  10 — of 

*  It  may  at  first  sight  appear  that  we  have  thus  proved  that  equal  masses 
have  equal  weights.  This  proposition  will  be  shown  to  be  true,  but  we  can  not 
prove  it  until  after  we  have  defined  equal  forces.  As  yet  we  have  not  shown  that 
the  spring  can  not  be  equally  stretched  by  unequal  f orqes  of  different  kinds. 


STANDARD  MASS.  81 

equal  masses,  which  will  be  J,  -J-,  ^  of  the  original  mass ;  or 
we  can  produce  masses  two,  three,  and  ten  times  as  great  as 
the  original.  It  is  in  this  way  that  the  graded  sets  of  masses 
are  originally  arrived  at.  Such  sets  of  masses  are  commonly 
spoken  of  as  "sets  of  weights,"  as  they  are  used  in  the 
process  called  weighing.  This  process  depends  upon  prin- 
ciples respecting  the  equality  and  measurement  of  forces, 
and  will,  therefore,  be  described  after  they  are  discussed 
(page  86). 

In  order  to  enable  men  all  over  the  world  and  at  all  times  to  make 
measurements  of  mass  which  will  be  comparable  with  one  another,  it  is 
essential  that  they  should  use  as  a  basis  of  their  measurements  the 
same  quantity  of  matter.  This  is  accomplished  by  having  a  standard 
mass  in  terms  of  which  all  masses  are  expressed. 

Standard  Mass. — As  a  standard  quantity  of  matter 
with  which  to  compare  all  other  masses,  we  may  adopt  any 
given  piece  of  matter  which  we  choose.  For  instance,  we 
may  select  a  particular  orange  as  our  standard  quantity. 
We  should  then  say  that  any  object  having  twice  as  much 
matter  as  the  orange  would  have  twice  the  standard  mass, 
and  so  on ;  but  the  orange  is  perishable  and  would  need  to 
be  replaced  from  time  to  time,  while  our  design  in  fixing  a 
standard  is  to  have  a  mass  for  reference  so  that  measure- 
ments of  mass  made  by  one  person  may  be  comparable  with 
those  made  by  another,  and  those  made  to-day  may  be  com- 
parable with  those  made  a  century  hence.  Therefore  our 
standard  mass  must  be  as  nearly  imperishable  and  un- 
changeable as  possible,  and  must  be  carefully  preserved. 

There  are  two  fundamental  standard  masses  to  which  all 
measurements  in  most  civilized  countries  are  referred.  One 
is  a  piece  of  platinum  carefully  preserved  by  the  French 
Government  at  Paris  and  called  the  "Kilogramme  des 
Archives"  (kilogramme  of  the  archives).  The  other  is  a 
piece  of  platinum,  in  the  office  of  the  Exchequer  at  Lon- 
don, called  the  Standard  Pound. 

Very  careful  determinations  have  shown  that  the  mass 


82  MASS,   FORCE,   ENERGY,  AND   WORK. 

of  the  standard  kilogramme  is  2-2046212  times  the  mass  of 
the  standard  pound,  so  that  the  pound  is  equal  to  0-45359265 
kilogrammes. 

Copies  of  these  standards  in  platinum  and  in  other  metals — i.  e., 
pieces  having  as  nearly  as  possible  the  same  mass  as  the  standards,  are  in 
the  possession  of  various  governments  and  are  made  the  legal  standards 
of  the  various  countries.  The  copies  belonging  to  our  Government  are 
in  the  keeping  of  the  United  States  Coast  and  Geodet'ic  Survey  at 
Washington,  D.  C.  The  original  standards  and  these  chief  copies  are 
used  only  occasionally  in  order  to  protect  them  from  wear  arid  acci- 
dental injury.  Secondary  copies  made  from  them  are  in  general  use. 

NOTE.— Platinum  is  used  in  these  standards  as  being  the  least  perishable  and 
changeable  of  all  the  metals. 

QUESTIONS. — What  is  mass  ?  In  measuring  mass,  force,  energy,  etc.,  what  are 
we  obliged  to  take  as  a  starting-point  ?  Define  equal  masses.  Why  can  we  not 
say  equal  forces  instead  of  "  the  same  force"  in  this  definition  ?  What  is  the 
readiest  means  of  applying  the  same  force  at  different  times  ?  Would  any 
other  force  than  weight  lead  to  the  same  results  if  it  were  equally  steady  ? 
How  do  we  arrange  to  apply  the  same  force  successively  to  different  masses  in 
the  cart  experiment  ?  In  any  case  what  is  the  total  amount  of  matter  to  be 
moved  in  an  experiment  with  the  cart  ?  What  kind  of  motion  does  a  constant 
force  produce  on  a  constant  mass  ?  How  is  this  illustrated  by  the  cart  experi- 
ment ?  How  does  the  rate  of  acceleration  by  the  same  force  vary  as  the  mass 
varies  ?  How  is  this  shown  by  the  cart  experiment  ?  If  the  cart  moves  from 
one  mark  to  the  next  in  two  seconds  on  one  occasion  and  in  one  second  on  an- 
other, how  great  is  the  rate  of  acceleration  in  the  second  instance  as  compared 
with  that  in  the  first  ?  Why? 

How  can  equal  masses  be  measured  off  by  the  cart  experiment  ?  Can  a  quantity 
of  air  and  a  quantity  of  lead  have  the  same  mass  ?  After  the  construction  of 
two  or  more  equal  masses  by  the  cart,  what  important  proposition  is  next 
proved  ?  How  can  we  construct  equal  masses  by  applying  this  proposition  ? 
How  can  we  construct  a  graded  set  of  masses  ?  Why  are  sets  of  masses  usu- 
ally called  sets  of  weights  ?  What  is  the  object  in  having  a  standard  of  mass  ? 
What  is  the  chief  quality  necessary  in  such  a  standard  ?  Name  and  describe 
the  two  chief  standards  in  general  use. 


MEASUREMENT  OF  FORCES. 

Equal  Forces. — We  must  now  learn  how  to  measure 
forces — that  is,  how  to  compare  the  magnitude  of  one  force 
with  that  of  another.  That  action  of  energy  which  we  call 
force  is  most  naturally  recognized  (page  46)  by  the  accelera- 
tion produced  in  free  bodies,  its  amount  may  be  measured 


EQUAL  MASSES,  EQUAL  WEIGHTS.  83 

by  the  amount  of  acceleration  it  causes ;  but  the  accelera- 
tion produced  by  a  given  force  has  already  been  proved  by 
experiment  (page  80)  to  vary  with  the  mass  accelerated. 
Hence,  in  measuring  forces,  both  the  mass  moved  and  the 
rate  of  acceleration  must  be  taken  into  account.  Let  us 
start,  then,  with  the  following  definition : 

Forces  are  equal  when  they  can  produce  equal  accelera- 
tions upon  the  same  or  equal  masses. 

Equal  Masses  have  Equal  Weights. — We  may  apply 
this  definition  in  connection  with  the  cart  experiment  to 
prove  the  proposition  that  equal  masses  have  equal  weights. 

Take  several  equal  masses  of  any  kind  and  of  suitable  amount. 
Prove  that  they  are  equal  masses  by  ascertaining  that  they  stretch 
the  spring-balance  equally,  or  that  they  counterpoise  each  other  on  the 
equal-arm  balance.  Put  one  of  them  into  the  pan  at  W.  Load  the 
cart  until  the  weight  at  W  produces  a  convenient  acceleration.  Time 
the  passage  from  A  to  B  as  before.  Remove  the  mass  from  the  pan 
and  put  in  another  of  the  equal  masses.  Time  again  from  A  to  B. 
Repeat  with  a  third  of  the  equal  masses.  The  times  will  all  be  found 
equal ;  but  the  mass  moved  was  equal  in  all  cases,  being  the  total 
mass  of  (cart  +  load -{- pan -j- mass  in  pan);  therefore,  by  the  defi- 
nition of  equal  forces,  the  forces  causing  these  equal  accelerations 
must  have  been  equal.  What  were  the  forces?  The  weight  of  the 
pan  plus  that  of  one  of  the  equal  masses.  These  total  weights  were 
then  constant ;  but  the  weight  of  the  pan  was  the  same  in  each  case ; 
hence  the  weights  of  the  equal  masses  must  also  have  been  equal.  The 
same  result  would  be  found  with  any  equal  masses  of  whatever  mate- 
rial. We  may,  therefore,  conclude  that  at  the  same  point  on  the 
earth's  surface  equal  masses  have  equal  weights. 

We  have  thus  a  means  of  obtaining  a  force  of  any 
amount  which  we  may  desire,  for  the  weight  of  two  equal 
masses  is  thus  proved  to  be  twice  that  of  one  of  the  masses, 
and  so  on.  For  instance,  if  we  desire  to  obtain  a  force  of 
say  23*2  times  that  of  the  weight  of  one  of  the  above  masses, 
we  have  only  to  put  together  twenty-three  and  one  fifth  of 
the  equal  masses,  and  the  weight  of  these  will  be  the  desired 
force.  This  gives  us  one  easy  and  exact  method  of  measur- 


84:  MASS,  FORCE,   ENERGY,   AND  WORK. 

ing  forces,  for  we  have  only  to  balance  the  forces  to  be 
measured  against  the  weight  of  known  masses.  We  must 
remember,  however,  that  the  weight  of  a  given  mass  is  not 
precisely  the  same  at  all  parts  of  the  earth's  surface,  as  fur- 
ther stated  on  page  91. 

While  the  experiments  with  the  cart  serve  to  illustrate  roughly 
the  law  that  equal  masses  have  equal  weights,  yet  for  scientific  pur- 
poses more  exact  proofs  are  necessary.  These  were  first  obtained  by 
Newton  through  experiments  with  pendulums  of  different  materials, 
and  have  since  been  verified  in  a  great  variety  of  ways. 

Spring-Balance  or  Dynamometer,  for  Measure- 
ment of  Forces. — The  spring-balance  is  really  an  instru- 
ment for  measuring  forces,  and  is  therefore 
called  a  dynamom'eter  (force-measurer).  One 
form  of  it,  represented  in  Fig.  22,  consists  of 
a  coiled  or  spiral  spring,  whose  upper  end 
is  secured  to  the  top  of  the  apparatus,  and 
whose  lower  end  is  attached  to  a  straight  rod 
carrying  an  index  or  pointer  and  having  a 
hook  at  the  bottom.  If  an  object  is  hung 
upon  the  hook,  its  weight  stretches  the  spring 
by  a  certain  amount  and  holds  the  index 
steadily  at  some  point  along  the  scale,  thus 
indicating  the  weight  of  the  object. 

This  scale  is  originally  graduated  by  hanging 
upon  the  hook  various  known  masses  and  marking 
their  weights  opposite  the  index.  For  instance,  a 

FIG.  22.— SPRING-  mass  of  one  pound  is  suspended  and  a  mark  made 
opposite  the  index.  A  mass  of  two  pounds  is  then 

attached  and  another  mark  made,  and  so  on ;  or  kilogrammes  may  be 

used  instead  of  pounds  if  the  metric  system  of  weights  is  preferred 

(see  page  540). 

If  an  object  of  unknown  weight  is  hung  on  the  hook, 
the  index  will  stand  at  a  certain  position.  Suppose  this 
happens  to  be  half-way  between  the  three  and  the  four 
pound  mark.  Then  the  weight  of  the  object  is  equal  to  the 


MEASUREMENT  BY  EQUAL-ARM  BALANCE.         85 

weight  of  a  mass  of  3*5  pounds,  or,  we  may  say,  for  brev- 
ity, its  weight  is  3*5  pounds.  If  any  other  force  than  a 
weight  stretches  the  spring,  then  the  index-reading  gives 
the  amount  of  that  force.  For  instance,  suppose  that  the 
balance  were  horizontal,  and  that  a  piece  of  iron  were  fast- 
ened to  the  hook  with  a  magnet  beyond  it,  and  that  their 
mutual  attraction  stretched  the  spring  so  that  the  index 
stood  at  the  four  pounds  mark.  Then  we  should  know 
that  the  force  of  attraction  between  the  iron  and  the 
magnet  was  equal  to  the  weight  of  a  mass  of  four  pounds. 
Similarly  we  might  measure  any  kind  of  constant  force.* 

Weights  by  Equal- Arm  Balance. — For  reasons  which 
will  be  explained  when  the  instrument  is  described,  the 
equal-arm  balance  swings  evenly  when  the  weights  of  the 
objects  in  the  two  pans  are  equal.  The  usual  method  of 
weighing  is  to  place  the  object  to  be  weighed  in  one  pan, 
and  in  the  other  to  put  masses  from  a  graded  set,  changing 
these  until  the  balance  swings  equally  on  each  side  of  its 
position  of  rest.  The  weight  of  the  object  is  then  equal  to 
the  weight  of  the  known  masses  in  the  other  pan. 

It  is  sometimes  possible,  but  seldom  convenient,  to  ar- 
range such  a  balance  for  measuring  other  forces  than  weight. 

The  process  of  weighing  is  one  capable  of  great  precision  and  deli- 
cacy. Equal-arm  balances  have  been  constructed  which  show  a  differ- 
ence of  one  ten-millionth  part  of  the  whole  load  on  the  pan. 

Measurement  of  Masses  by  the  Equal-Arm  Bal- 
ance and  by  the  Spring-Balance. — As  equal  masses 
have  equal  weights,  it  is  evident  that  the  equal-arm  balance 
enables  us  to  measure  masses  easily  in  terms  of  a  graded  set 

*  Observe  that  the  pound,  like  the  kilogramme,  originally  and  properly  de- 
notes a  certain  mass  of  matter,  but  that  for  convenience  in  speaking  of  weights 
we  say  "the  weight  of  a  pound,"  or  of  a  kilogramme,  instead  of  using  the  cor- 
rect but  longer  phrases,  " the  weight  of  a  pound  of  matter,11  "the  weight  of  a 
pound-mass,11  etc.  So  in  the  case  of  other  forces,  we  speak  of  "  a  force  of  one 
pound,"  meaning  "  a  force  equal  to  the  weight  of  a  pound  of  matter."  It  is  im- 
portant to  keep  this  in  mind  to  avoid  confusion. 


86  MASS,  FORCE,  ENERGY,   AND   WORK. 

of  masses.  When  the  weights  in  the  two  pans  are  equal,  the 
masses,  of  course,  are  equal. 

For  instance,  if,  to  balance  a  certain  object,  it  is  neces- 
sary to  use  a  two-pound,  a  one-pound,  and  a  half-pound 
mass  in  the  other  pan,  the  object  has  a  weight  equal  to  that 
of  a  mass  of  3-5  pounds.  Its  mass  is  thus  shown  to  be  3'5 
times  the  mass  of  a  standard  pound. 

To  produce  the  same  Acceleration  011  Different 
Masses,  the  Force  must  be  proportional  to  the  Mass 

moved. — Put  on  the  cart  a  small  load,  and  on  W  enough 
weight  to  produce  a  convenient  acceleration.  Time  the  pas- 
sage from  A  to  B.  Weigh  W,  also  the  cart  and  contents 
together  with  W. 

Double  the  force  at  W  and  add  to  the  load  upon  C  until  it 
goes  from  A  to  B  in  just  the  same  time  as  before,  and  hence 
has  the  same  acceleration.  Weigh  C  and  W  together  again. 
The  weight,  and  therefore  the  mass,  will  be  found  to  be 
twice  as  great  as  before. 

Double  the  force  at  W  and  double  the  total  mass,  and  observe  that 
the  cart  passes  from  A  to  B  in  the  same  time  as  before.  Make  W  and 
the  total  mass  five  times  as  great  as  at  first,  and  notice  that  the  cart 
still  travels  from  A  to  B  in  the  same  time.  Hence,  to  produce  the 
same  acceleration  on  different  masses  the  force  must  be  proportional  to 
the  mass  moved. 

Acceleration  of  Constant  Mass  proportional  to 
the  Force. — Load  the  cart  rather  heavily.  Put  on  a  load  at 
W  which  will  give  a  slow  motion.  Time  the  movement  from 
A  to  B  as  before.  Next  weigh  W — i.  e.,  pan  and  contents. 
Take  from  the  load  of  C  a  weight  equal  to  three  times  W, 
and  put  it  into  the  pan  in  addition  to  the  former  load.  We 
know  then  that  we  have  made  the  force  at  W  four  times  as 
great,  but  have  not  changed  the  whole  mass  to  be  moved. 
Time  the  motion  from  A  to  B  again.  You  will  find  the 
space  is  traversed  in  half  the  time. 

What  was  the  acceleration  here  ?  From  the  laws  of  accelerated 
motion  (page  20),  we  know  that  when  the  time  of  passing  over  the 


NEWTON'S  SECOND  LAW  OF  MOTION.  87 

same  space  is  one  half  as  great,  the  acceleration  is  four  times  as  great. 
If  we  make  the  force  (weight  at  W)  nine  times  as  great  as  at  first,  the 
time  will  be  found  to  be  one  third,  and  therefore  the  acceleration  to  be 
nine  times  as  great,  and  so  on. 

Thus  the  acceleration  of  the  same  mass  is  four  times  as  great  when 
the  force  is  four  times  as  great,  and  nine  times,  when  the  force  is 
nine  times — that  is,  with  a  constant  mass,  the  acceleration  is  directly 
proportional  to  the  force  applied. 

A  Constant  Force  is  proportional  to  the  Product 
of  the  Mass  into  the  Acceleration  produced  by  it 
upon  that  Mass. — The  statements  of  the  two  foregoing 
paragraphs  may  be  combined  in  one,  viz.,  that  to  produce  in 
a  given  mass  a  given  acceleration,  the  force  must  be  propor- 
tional to  the  product  of  the  mass  into  the  acceleration. 

For  instance,  suppose  that  we  begin  with  a  given  mass  and  force. 
This  force  will  produce  a  certain  acceleration.  If  we  double  the  mass, 
twice  the  force  will  be  necessary  to  produce  the  same  acceleration ;  but 
if  we  desire  to  increase  the  acceleration,  say  to  treble  it,  we  must  also 
treble  the  force.  Hence,  to  give  the  double  mass  a  trebled  accelera- 
tion, we  must  apply  six  times  the  first  force.  To  make  a  mass  five 
times  as  great  as  the  given  mass  move  with  seven  times  the  accelera- 
tion, would  require  a  force  of  5  x  7  =  35  times  the  first,  and  so  on. 

Conversely,  if  a  body  is  seen  to  be  moving  with  a  uniform 
acceleration,  we  know  that  it  must  be  under  a  uniform  force 
proportional  to  the  product  of  its  mass  into  its  acceleration. 

Newton's  Second  Law  of  Motion. — The  universal 
experience  in  regard  to  the  direction  and  amount  of  effect 
of  forces  is  stated  in  Newton's  second  law  of  motion. 

"  Change  of  Motion  is  proportional  to  the  impressed 
force,  and  takes  place  in  the  direction  of  the  straight  line  in 
which  the  force  acts." 

In  this  law,  "  change  of  motion  "  means  the  product  of 
the  mass  into  the  acceleration  produced  by  the  action  of  the 
force  in  question  upon  a  free  body  of  the  given  mass. 

Units. — When  we  measure  a  quantity  of  any  kind,  we 
express  it  in  terms  of  a  unit — that  is,  a  definite  quantity — of 


88  MASS,  FORCE,  ENERGY,  AND  WORK. 

the  same  kind.  If,  for  instance,  we  say  that  the  side  of 
a  room  is  eighteen  feet  long,  we  mean  that  its  length  is 
eighteen  times  the  length  which  we  call  a  foot.  If  we  say 
that  two  towns  are  23 -54  miles  apart,  we  mean  that  their 
distance  apart  is  twenty-three  and  T%-  times  the  distance 
which  we  call  a  mile.  Here  the  foot  was  the  unit  of  dis- 
tance in  the  first  case,  and  the  mile  the  unit  of  distance  in 
the  second.  We  might  have  expressed  either  distance  in 
inches,  yards,  rods,  metres,  kilometres,  or  any  other  unit 
which  we  chose  to  use.  Thus  the  choice  of  a  unit  is  wholly 
arbitrary.  We  can  select  a  unit  of  such  size  as  to  be  con- 
venient for  the  purpose  in  hand,  and  there  may  be,  and  usu- 
ally are,  many  different  sized  units  of  the  same  kind,  as  just 
shown  for  units  of  length. 

But  it  should  be  remembered  that  units  for  measuring 
the  same  kind  of  quantity  are  all  and  always  of  the  same 
kind  as  that  quantity,  and  are  merely  arbitrarily  chosen 
amounts  of  that  quantity.  They  differ  only  in  size.  Thus, 
the  inch,  foot,  metre,  mile,  etc.,  are  a  few  of  the  various  units 
of  length.  They  are  all  the  same  kind  of  thing,  viz.,  distances. 
They  differ  only  in  size.  Similarly,  the  quart,  litre,  gallon, 
hogshead,  gill,  etc.,  are  units  of  capacity;  they  differ  in 
nothing  but  magnitude.  This  is  true,  however  complicated 
the  nature  of  the  quantity  measured. 

The  Idea  of  Standards  must  be  kept  distinct  from 
that  of  units.  A  standard  yard  is  merely  a  metallic  bar 
with  lines  ruled  upon  it,  whose  distance  apart  at  a  stated 
temperature  is  defined  by  law  to  be  one  yard.  The  yard  is 
used  as  a  unit  of  length.  It  is  not,  however,  the  only  unit 
of  length,  and  in  fact  is  merely  a  fixed  distance  by  reference 
to  which  various  other  units  of  length  can  be  defined  and 
reproduced.  Thus,  the  foot  is  equal  to  one  third  of  that 
distance,  the  mile  is  equal  to  5,280  such  feet,  etc. 

The  standard  metre  is  a  bar  of  platinum  preserved 
by  the  French  Government  at  Paris,  having  lines  ruled 


UNITS.  89 

upon  it  whose  distance  apart,  at  a  stated  temperature,  is 
denned  by  law  to  be  one  metre.  This  distance  is  about 
3-4  inches  longer  than  the  yard.  The  metre  is  exactly 
39-3702  inches. 

We  may  use  any  multiple  or  submultiple  of  these  stand- 
ard distances  which  we  choose  as  units  in  any  particular 
case,  or  indeed  any  other  distances ;  but,  in  order  that  our 
measurements  should  convey  an  exact  idea  to  others,  they 
must  be  expressed  in  units  whose  relation  to  the  standards 
is  accurately  known. 

The  standard  pound  and  the  standard  kilogramme  are,  as  has  been 
stated,  standard  masses ;  but  neither  is  commonly  used  as  the  unit 
of  mass.  For  reasons  which  will  appear,  the  units  of  mass  actually 
employed  are  either  larger  or  smaller  than  these  standards,  but  bear  a 
perfectly  definite  and  known  ratio  to  them.  In  the  following  para- 
graphs, the  scientific  units  will  be  defined  and  described  first.  The 
engineering  and  other  units  will  be  summarized  later. 

Unit  of  Length. — In  scientific  work  the  unit  of  length 
generally  employed  is  the  centimetre,  viz.,  the  one-hundredth 
part  of  the  standard  metre. 

The  Unit  of  Time  commonly  adopted  is  the  second. 

The  Unit  of  Mass  employed  in  almost  all  scientific 
work  is  the  mass  of  one  gramme,  or  the  one-thousandth  part 
of  the  mass  of  the  standard  kilogramme. 

Instrument-makers  supply  graded  sets  of  masses.  These  may  con- 
tain any  amounts  desired.  A  convenient  set  contains  pieces  of  one 
kilogramme,  and  of  500,  200,  200,  100,  50,  20,  20,  10,  5,  2,  2, 1  grammes, 
and  so  on,  for  such  decimals  as  are  desired. 

The  system  of  units  based  on  the  centimetre,  gramme, 
and  second,  is  called  the  centimetre-gramme-second  system, 
or  the  C.  G.  S.  System.  In  computations  where  this  system 
is  to  be  employed,  all  quantities  of  length,  mass,  or  time, 
must  be  reduced  to,  and  expressed  in,  centimetres,  grammes, 
or  seconds,  before  being  used.  A  similar  statement  holds 

good  for  any  other  system. 

7 


90  MASS,  FORCE,  ENERGY,  AND  WORK. 

The  Unit  of  Force,  in  all  systems,  is  a  force  which  will 
produce  unit  acceleration  upon  unit  mass.  In  the  C.  G.  S. 
system,  the  unit  acceleration  is  one  centimetre  per  second. 
The  unit  of  force — C.  G.  S. — is  then  a  force  which  can  pro- 
duce an  acceleration  of  one  centimetre  per  second  on  a  mass 
of  one  gramme.  This  unit  of  force  is  called  the  Dyne. 

Any  constant  force  F,  which  is  producing  in  a  mass  of  M  grammes 
an  acceleration  of  a  centimetres  per  second,  must  be  equal  to  MX  a 
dynes  (i.  e.,  F  =  Ma) ;  for  to  produce  on  a  mass  of  M  grammes  an  ac- 
celeration of  one  centimetre  per  second,  would  require  M  dynes.  To 
produce  on  the  same  mass  an  acceleration  of  a  centimetres  per  second 
would  require  a  times  this  force — i.  e.,  Ma  dynes — or,  in  any  system 
of  units,  to  produce  an  acceleration  of  a  units  on  a  mass  of  M  units 
would  require  a  force  of  Ma  units. 

EXAMPLE. — Suppose  that  we  observe  a  body  moving  with  a  uni- 
form acceleration  of  250  centimetres  per  second,  and  find  by  the  bal- 
ance that  the  body's  mass  is  400  grammes.  What  is  the  amount  of 
the  force  producing  the  acceleration  ?  F  =  Ma  =  100,000  dynes. 

To  obtain  an  idea  of  how  large  this  unit  of  force  is  as 
compared  with  that  very  familiar  force,  the  weight  of  some 
standard  body,  we  may  take  a  body  whose  mass  is  one 
gramme  and  let  it  drop  from  a  height.  It  will  be  accel- 
erated by  a  constant  force,  its  weight,  and  will  therefore 
fall  with  a  uniformly  accelerated  motion.  By  exact  experi- 
ment, that  acceleration  is  found  to  be  in  the  latitude  of 
Boston,  and  at  the  level  of  the  sea,  about  980-4  centimetres 
per  second.  The  force  with  which  the  mass  of  one  gramme 
is  drawn  toward  the  earth — i.  e.,  the  weight  of  a  gramme — 
is  then  much  greater  than  one  dyne.  A  dyne  would  have 
given  it  an  acceleration  of  only  one  centimetre  per  second, 
but  it  received  an  acceleration  of  980-4  centimetres  per 
second.  We  have  proved  that  the  force  is  proportional  to 
the  acceleration.  Hence  this  force  must  have  been  equal 
to  980-4  dynes;  or,  to  state  it  in  another  way,  F=Ma. 
M=l  gramme,  a  =  980-4  centimetres  per  second,  F=  I  X 
980-4  =  980-4  dynes.  The  weight  of  the  gramme  is,  there- 
fore, 980-4:  dynes  in  latitude  42°  at  sea-level. 


WEIGHT  DIFFERS  WITH  LATITUDE.  91 

We  thus  have  an  easy  way  of  producing  the  dyne  at  any  time. 
Take  the  mass  of  ^th  of  a  gramme.  This  mass  will  be  attracted 
toward  the  earth  by  a  force  of  exactly  one  dyne.  You  will  see  from 
this  also  that  a  body  whose  mass,  as  found  by  the  balance,  is  M 
grammes,  weighs  980  x  M  dynes.  For  instance,  a  body  whose  mass  is 
300  grammes  weighs — i.  e.,  is  attracted  to  the  earth  by  a  force  of — 980 
x  300  =  294,000  dynes.  The  dyne  is  thus  a  very  small  force.  It  is  con- 
venient for  much  scientific  work,  especially  in  electricity  and  magnet- 
ism, but  is  not  so  for  engineering  work  where  large  forces  are  to  be 
dealt  with.  A  more  convenient  unit  for  such  work  is  described  later. 

It  is  a  fact  of  importance  that  if  the  mass  of  a  gramme  is  dropped 
near  the  sea-level  at  the  equator,  it  will  have  an  acceleration  of  only 
978-1  centimetres  per  second  ;  at  latitude  45°  sea-level,  the  accelera- 
tion would  be  980-6  centimetres  per  second ;  at  the  pole,  it  would  be 
983-1  centimetres  per  second.  The  letter  g  is  commonly  used  to  de- 
note the  acceleration  due  to  weight.  This  acceleration  is  found  to  be 
very  slightly  less  above  the  sea-level ;  for  example,  at  45°  sea-level 
it  is  980-6,  but  at  1,000  feet  above  the  sea  it  is  about  980-5.  As  has 
been  shown,  it  is  due  to  the  weight  of  the  body.  If,  therefore,  the 
same  body  be  taken  to  various  places,  its  acceleration  will  be  different, 
and  its  weight  will  be  different  in  the  same  proportion.  Thus,  the 
weight  of  the  same  or  an  equal  mass  at  the  equator  is  about  jfoth 
part  less  than  that  at  the  poles.  In  general,  the  weight  in  dynes  of 
a  gramme  at  any  place  where  the  acceleration  of  gravity  is  g,  will  be 
g  dynes. 

To  measure  the  Force  with  which  a  body  is  attracted 
to  the  earth — i.  e.,  to  ascertain  its  weight — we  may  put  it 
into  one  pan  of  an  equal-arm  balance  (page  163)  and  place 
in  the  other  pan  standard  masses  until  we  have  just  enough 
to  counterbalance  it.  Thus  the  weight  of  the  masses  just 
equals  that  of  the  body.  Suppose  we  count  up  the  standard 
masses  used,  and  find  them  to  be  340  grammes.  We  know 
then  two  things:  first,  that  the  mass  of  the  body  is  340 
grammes ;  second,  that  the  weight  of  the  body  is  340  X  g 
dynes ;  and,  knowing  g  to  be  980-4  centimetres  per  second, 
we  know  that  the  weight  is  340  X  980  =  333,200  dynes. 

It  is  confusing  to  students  when  they  first  notice  that  all  bodies, 
whatever  their  mass,  fall  to  the  earth  with  equal  acceleration  ;  but  it 
is  easily  understood  by  considering  that  the  weight  is  proportional  to 


92  MASS,  FORCE,  ENERGY,  AND  WORK. 

the  mass,  so  that,  although  the  force  causing  the  heavier  body  to  fall 
is  greater,  the  mass  to  be  accelerated  is  greater  in  the  same  propor- 
tion. Hence  the  acceleration  must  be  the  same.  Prove  this  by  drop- 
ping, side  by  side,  objects  of  equal  and  different  weights. 

The  spring-balance  has  been  described  as  a  convenient  instrument 
for  measuring  forces.  In  order  that  it  may  measure  them  directly  in 
terms  of  the  C.  G.  S.  unit,  it  should  be  graduated  by  hanging  upon  it 
masses  of  ^f^,  ^f^,  etc.,  grammes,  as  the  weights  of  these  masses  are  1 
dyne,  2  dynes,  etc. 

But  as  any  unit  of  force  differs  from  the  dyne  only  in  amount,  we 
may  use  a  balance  graduated  in  any  unit  and  reduce  to  dynes  by  mul- 
tiplying by  a  suitable  factor.  Thus,  the  weight  of  the  standard  pound 
at  London  is  equal  to  about  44,500,000  dynes.  If  a  force  were  meas- 
ured by  a  spring-balance  graduated  at  London  in  pounds  and  found 
to  be  2-1  pounds,  the  force  would  be  about  93,450,000  dynes. 

Momentum. — If  a  body,  of  mass  J/,  is  moving  with  a 
velocity  F,  the  product  M  V  of  its  mass  by  its  velocity  is 
called  the  Momentum  of  the  body. 

The  momentum  is  equal  to  the  product  Ft  of  the  force  into  the 
time ;  or  M  V  =  Ft.  Therefore,  F=MV+t.  For  V  =  at  and  F  = 
Ma  .'.  F=Mv  +  t  or  Mv  =  Ft. 

EXAMPLE. — If  a  body  with  a  mass  of  10  grammes  is  moving  with 
a  velocity  of  5  centimetres  per  second,  then  its  momentum  would  be 
M  V=  10  x  5  =  50  units.  This  momentum  might  have  been  produced 
by  any  uniform  force  F  acting  for  a  suitable  time  t.  If  it  had  been 
produced  in  t  =  2  seconds,  then  the  force  must  have  been  F  =  M  V  -5-  t 
=  50  -r-  2  =  25  dynes ;  if  in  a  time  of  0-002  second,  then  the  force 
must  have  been  F  =  50  -f-  -002  =  25,000  dynes;  if  it  had  been  pro- 
duced by  a  force  of  5  dynes,  the  time  during  which  the  force  must 
have  acted  would  have  been  t  =  MV-r-  F  =  50  -5-  5  =  10  seconds. 

If  the  force  causing  the  momentum  is  not  constant,  then  the  force 
computed  by  the  expression  above  would  be  the  average  value  of  the 
force  during  the  time  t.  The  average  value  is  that  amount  which  we 
should  find  if  we  could  divide  the  time  into  extremely  small  intervals, 
and  could  find  the  amount  of  the  force  at  the  middle  of  each  interval, 
and  should  then  take  the  average  of  all  these  values — that  is,  add 
them  all  together  and  divide  the  sum  by  their  number. 

Impulse. — The  product  Ft  of  the  force  into  the  dura- 
tion of  its  action  is  called  its  Impulse.  It  has  just  been 


IMPULSE.  93 

shown  that  Ft  =  M F,  hence  we  may  say  that  the  impulse 
of  a  force  is  measured  by  the  momentum  produced.  There 
are  many  cases  in  which  forces  act  for  short  times  only,  as 
when  the  gases  caused  by  the  burning  powder  in  a  gun  are 
forcing  out  the  bullet,  or  the  bowstring  is  speeding  the 
arrow,  or  one  elastic  body  strikes  another,  as  when  a  ball  is 
struck  by  a  bat.  In  such  cases,  the  force  is  not  constant  but 
varies  rapidly,  besides  being  of  very  brief  duration.  Here 
we  can  not  usually  know  either  t  or  F,  but  only  M  V,  so 
that  the  amount  of  the  impulse  is  found  from  MV. 

Time  required  to  set  Matter  in  Motion. — How- 
ever large  the  force  acting,  and  however  small  the  mass 
acted  upon,  some  time  is  required  to  impart  any  velocity. 

MV 

This  time  is  expressed  by  the  equation  t  =  —^-     If  M  and 

V  are  very  small  and  F  is  very  large,  t  will  necessarily  be 
small,  but  can  never  be  zero.  To  make  t  zero  would  require 
an  infinite  force  F,  and  anything  infinite  is  beyond  our 
physical  experience  and  beyond  our  powers  of  conception. 

QUESTIONS.— Define  equal  forces.  Prove  that  equal  masses  have  equal  weights. 
Does  this  fact  require  proof  ?  How  does  this  give  us  a  means  of  obtaining  any 
desired  amount  of  force  ?  Describe  the  spring-balance.  Why  is  it  called  a 
dynamometer  ?  How  is  the  scale  of  the  spring-balance  originally  graduated  ? 
How  would  you  use  a  spring-balance  to  measure  the  weight  of  a  body  ?  How 
would  you  use  it  to  measure  some  force  not  in  a  vertical  direction  ?  In  such  a 
case,  would  you  have  to  make  any  allowance  for  the  effect  of  the  weight  of  the 
parts  of  the  balance  itself  ? 

Is  the  standard  pound  a  mass  or  a  weight  ?  What  is  weight  ?  When  we  speak 
of  a  force  of  one  pound,  what  do  we  mean  ?  Describe  the  process  of  obtaining 
the  weight  of  an  object  by  an  equal-arm  balance.  Is  it  a  process  capable  of  ac- 
curacy ?  How  does  the  process  of  measuring  the  mass  of  an  object  by  a  bal- 
ance differ  from  that  of  measuring  its  weight  ?  By  an  experiment,  2'5  pounds 
are  found  necessary  to  balance  an  object ;  state  in  full  what  the  weight  of  the 
object  is  and  what  its  mass  is.  Why  and  how  much  is  the  spring- balance  in 
error  when  used  at  other  places  than  that  for  which  it  is  graduated  ? 

If  one  mass  is  four  times  another,  how  many  times  as  much  force  is  necessary  to 
produce  upon  it  a  given  acceleration  ?  Define  acceleration.  If  to  a  given  body 
you  apply  successively  forces  of  2  and  4,  what  will  be  the  relative  accelerations  ? 
What  is  the  relation  between  the  force  and  the  acceleration  produced  by  it 
upon  any  mass  ?  Is  this  true  of  any  but  a  free  body  ?  State  Newton's  second 
law  of  motion. 


94  MASS,  FORCE,  ENERGY,  AND  WORK. 

What  is  meant  by  a  unit  ?  What  determines  the  size  of  unit  selected  for  a  given 
purpose  ?  In  what  respect  do  different  units  of  the  same  kind  differ  ?  Do  they 
differ  in  any  other  respect  ?  What  is  the  scientific  unit  of  length  ?  Of  time  ? 
Of  mass  ?  What  is  the  C.  G.  S.  system  ?  In  what  units  must  lengths  be  ex- 
pressed before  being  used  in  computations  ?  Masses  ?  Times  ?  Why  ?  Define 
the  unit  of  force  in  general.  What  is  the  C.  G.  S.  unit  of  force  called  ?  Define 
it.  Show  how  in  these  units  F=Ma. 

A  body  is  moving  with  an  acceleration  of  10  centimetres  per  second.  Its  mass  is 
found  by  the  balance  to  be  30  grammes.  What  is  the  force  acting  ? 

A  body  of  a  mass  of  20  grammes  is  moving  under  a  constant  force  of  40  dynes. 
What  is  its  acceleration  ? 

An  object  under  a  force  of  50  dynes  is  receiving  an  acceleration  of  5  centimetres 
per  second.  What  is  its  mass  ? 

Show  what  the  weight  of  a  gramme  is  when  expressed  in  dynes  at  a  place  where 
the  acceleration  of  gravity  is  980  centimetres  per  second.  How  does  this  en- 
able us  to  obtain  a  force  of  any  desired  number  of  dynes  at  any  place  ? 

What  is  the  weight  in  dynes  of  an  object  whose  mass  is  2  kilogrammes  at  a  place 
where  g  =  981  centimetres  per  second  ? 

Why  do  all  bodies,  whatever  their  mass,  tend  to  fall  under  gravity  with  equal 
acceleration  ?  If  a  body  were  found  by  a  spring-balance  to  have  a  weight  of 
3  pounds  avoirdupois,  what  would  be  the  force  in  dynes  with  which  it  is  at- 
tracted to  the  earth  ? 

Define  momentum.  Prove  that  the  momentum  produced  by  a  constant  force 
acting  for  a  given  time  is  equal  to  the  product  of  the  force  into  the  time. 

A  body  of  a  mass  of  20  grammes  is  moving  with  a  velocity  of  30  centimetres  per 
second.  What  is  its  momentum  ?  If  this  momentum  were  produced  in  5  sec- 
onds, how  great  must  be  the  constant  force  required  ?  If  it  had  been  produced 
by  a  constant  force  of  15  dynes,  how  long  must  that  force  have  acted  upon  the 
body  ?  Suppose  the  force  had  been  variable  and  had  produced  this  momentum 
in  10  seconds,  what  must  have  been  the  average  amount  of  the  force  ? 

Define  Impulse.    Can  a  finite  force  produce  motion  in  no  time  ? 

A  ball  whose  mass  is  100  grammes  is  struck  by  a  bat  and  receives  a  velocity  of  20 
centimetres  per  second.  What  is  the  amount  of  the  impulse  ? 


MEASUREMENT  OF  ENERGY. 

Matter  and  Motion  are  the  only  Essentials  of 
Energy. — We  have  learned  that  matter  can  possess  energy 
only  by  being  in  motion.  We  know  also  that  for  an  onward- 
moving  body  the  energy  is  greater  as  the  mass  and  the  ve- 
locity are  greater.  This  has  been  shown  by  the  experiments 
with  the  rolling  balls,  and  is  illustrated  in  every-day  experi- 
ence. The  energy  of  a  body,  then,  depends  on  its  mass  and 
its  velocity. 

If  any  portion  of  matter  M  is  moving  with  a  velocity  V 
along  its  path  at  any  instant,  then  its  energy  E  at  that  in- 


MEASUREMENT  OF  ENERGY. 


stantis  equal  to  $MV*  —  that  is,  to  one  half  the  product  of 
its  mass  by  the  square  of  its  velocity. 

The  Unit  of  Energy  in  the  C.  G.  S.  system  is  the  Erg. 

Thus  a  mass  of  40  grammes  moving  with  a  velocity  of  10  centi- 
metres a  second  would  have  an  energy  of  £  x  40  x  102  =  2,000  ergs. 

Energy  of  Rotation.  —  A  body  may  be  rotating,  but 
yet  have  no  onward  motion.  In  such  a  case  each  particle  of 
the  body  possesses  at  any  given  instant  a  perfectly  definite 
velocity,  and  therefore  an  amount  of  energy  which  would 
be  denoted  by  \MV*,  where  M  is  the  mass  and  V  the  veloci- 
ty of  the  particle.  If  we  take  the  sum  of  all  these  quanti- 
ties for  the  whole  body,  that  sum  will  represent  the  total 
energy  of  rotation  of  the  body.  Rotation  and  onward  mo- 
tion can,  of  course,  exist  at  the  same  time,  so  that  a  body 
may  simultaneously  possess  energy  from  both  motions. 

The  heavy  fly-wheel  of  an  engine  in  motion  possesses  an  immense 
energy  of  rotation.  Slowing  down  the  speed  of  the  wheel  implies  that 
a  large  amount  of  energy  is  taken  from  it,  and  this  requires  some 
time.  Starting  it  again  similarly  requires  energy  and  time.  The  fly- 
wheel, therefore,  is  a  great  help  toward  keeping  the  speed  of  the  engine 
uniform.  Think  of  the  enormous  energy  of  rotation  of  the  earth  or 
of  the  sun  on  its  axis  ! 

MEASUREMENT  OF  WORK. 

Work  is  only  a  name  for  the  process  of  transfer  or 
transformation  of  energy.*  It  must,  therefore,  be  expressed 
in  the  same  unit  as  energy  —  that  is,  in  ergs.  Thus,  if  a  body 
has  imparted  to  it  an  amount  of  energy  equal  to  100  ergs, 
then  the  amount  of  work  done  upon  it  in  imparting  that 
energy  will  also  be  100  ergs  ;  and  the  amount  of  work  which 
the  body  can  do  in  giving  up  that  energy  will  be  100  ergs. 

*  For  the  sake  of  brevity  and  convenience,  we  use  the  expression  "  amount 
of  work  done,11  or  simply  "work  done,"  instead  of  "amount  of  energy  changed 
in  place  or  form.11  Remember  that,  when  we  speak  of  measuring  the  amount 
of  work  done,  we  mean  measuring  the  amount  of  energy  changed. 


96  MASS,  FORCE,  ENERGY,  AND  WORK. 

In  many  cases  where  the  energy  is  transformed  when  the  work  is 
done,  it  is  impossible  to  measure  directly  either  the  amount  of  energy 
given  up  by  the  body  doing  the  work,  or  the  amount  received  by  the 
body  upon  which  the  work  is  done.  For  instance,  if  you  raise  a  heavy 
body  from  the  ground  to  a  table,  you  expend  muscular  energy  and 
produce  potential  energy.  Now,  it  is  not  practicable  to  measure  the 
muscular  energy  directly  nor  the  energy  which  produces  the  condition 
which  we  call  potential  energy ;  but  we  have,  nevertheless,  a  means  of 
finding  how  much  energy  is  transformed,  as  will  now  be  shown. 

Work  against  or  by  a  Constant  Force. — If  a  body 
is  moved  through  a  distance  s  against  or  by  a  constant  force 
F,  the  amount  of  work  done  is  equal  to  the  product  of  the 
force  into  the  distance — it  may  be  expressed  by  W  =  Fs. 

EXAMPLES. — A  body  weighing  50  dynes  is  raised  vertically  through 
100  centimetres  against  gravity.  How  much  work  is  done  ?  W  = 
Fs  =  50  x  100  =  5,000  ergs. 

The  same  body  falls  freely  through  the  same  distance.  How  much 
work  is  done  I  W  =  Fs  =  50  x  100  =  5,000  ergs. 

A  body  whose  mass  is  40  grammes  falls  freely  through  10  centi- 
metres at  a  place  where  g  =  980  cm.  sec. ;  how  much  work  is  done 
upon  it  by  gravity  f  Its  weight  is  40  x  980  =  39,200  dynes.  The  work 
done  is  therefore  W  =  Fs  —  39,200  x  10  =  392,000  ergs. 

How  much  energy  would  it  possess  at  the  end  of  the  fall  I  392,000 
ergs.  Why  I 

Compute  the  energy  from  its  acquired  velocity.  E  =  %M F2.  M  — 
40  grammes.  By  the  laws  of  accelerated  motion,  F2  =  2  gs  =  2  x  980  x 
10  =  19,600  cm.  sec.  Therefore,  E  =  £  x  40  x  19,600  =  392,000  ergs. 
This  result  is  necessarily  the  same  as  that  obtained  by  the  other  method, 
for  the  two  formulae  Fs  and  \MV*  must,  of  course,  be  equivalent. 

How  much  work  must  be  done  to  stop  this  body  f    392,000  ergs. 

How  much  to  keep  it  moving  with  the  acquired  velocity?  None, 
if  there  is  no  resistance  to  motion.  How  high  would  it  rise  if  thrown 
vertically  upward  with  this  velocity  f 

The  Amount  of  Work  done  is  the  same,  whether 
the  body  is  moved  slowly  or  fast.  For  instance,  in  the  first 
of  the  examples  just  given,  the  amount  of  work  is  obviously 
the  same,  however  long  or  short  the  time  occupied  in  raising 
the  body  may  be.  The  amount  of  work  depends  only  on 
F  and  s,  and  neither  of  these  changes  with  the  time.  The 


AMOUNT  OF  WORK.  97 

rate  of  work  is  different ;  but  that  is  another  thing,  which 
will  be  separately  considered. 

The  amount  of  work  done  is  the  same  when  the  body 
moves  freely  and  thus  stores  up  the  energy  in  itself  as  en- 
ergy of  onward  motion,  and  when  the  body  moves  against 
resistance,  transforming  the  energy  or  transferring  it  to 
other  bodies.  The  "  weight "  of  a  clock  will  have  done  upon 
it  by  gravity  the  same  amount  of  work  in  the  course  of  its 
descent,  whether  it  drops  freely,  or  whether  it  descends  in 
its  usual  slow  manner,  continually  transferring  the  energy 
given  it  by  gravity  to  the  works  of  the  clock  where  (in  over- 
coming friction)  this  energy  is  transformed  mostly  into  heat. 

EXAMPLE. — A  clock-weight  has  a  mass  of  40  grammes,  and  de- 
scends in  a  day  through  10  centimetres.  How  much  work  is  done 
upon  it  by  gravity  ?  Gravity  does  upon  it  392,000  ergs  of  work  (see 
preceding  example)  whether  it  descends  slowly  or  falls  freely. 

The  Amount  of  Potential  Energy  relatively  to  a 
given  point,  which  belongs  to  a  body  because  of  its  position 
and  the  force  acting  upon  it,  is  equal  to  the  energy  which 
it  would  acquire  in  moving  freely  to  that  point,  or  to  the 
work  which  would  be  done  upon  it  by  the  force. 

The  potential  energy  of  the  clock- weight  at  its  starting  position 
relatively  to  a  point  10  centimetres  lower  would  be  392,000  ergs. 

Similar  computations  apply  to  other  kinds  of  force.  Weight  is 
selected  for  the  examples  because  it  is  convenient  and  familiar. 

QUESTIONS.— What  is  energy  ?  How  can  matter  possess  energy  ?  Is  there  more 
than  one  way  in  which  matter  can  possess  energy  ?  What,  then,  do  we  mean 
by  different  forms  of  energy  ?  What  is  potential  energy  ?  If  a  portion  of  mat- 
ter of  mass  m  has  a  velocity  v,  what  is  its  energy  ?  Relative  to  what  does  it 
possess  that  energy  ? 

What  is  an  erg  ?  The  air  in  an  ordinary  steam-car  has  a  mass  of  about  300 
pounds,  or  140,000  grammes.  Suppose  the  car  to  be  moving  at  a  rate  of  about 
21  miles  an  hour,  which  is  about  1,000  centimetres  per  second,  what  is  the  en- 
ergy of  the  air  relative  to  the  ground  ?  Suppose  the  car  itself  has  a  mass  of 
20  tons,  what  is  the  energy  of  the  air  as  compared  with  that  of  the  car  ? 

A  stone  whose  mass  is  500  grammes  is  moving  with  a  velocity  of  1,960  centimetres 
per  second.  What  is  its  energy  ? 

How  does  a  body  in  rotation  possess  energy  ?  Relatively  to  what  does  it  possess 
energy  ?  Do  its  parts  possess  energy  of  onward  motion  relative  to  one  another  ? 
Explain  the  action  of  a  fly-wheel. 


98  MASS,   FORCE,   ENERGY,   AND   WORK. 

What  is  work  ?  What  is  the  C.  G.  S.  unit  of  work  ?  How  much  work  must  be 
done  to  set  the  air  of  the  problem  above  into  motion  or  to  stop  it,  neglecting  all 
losses  ?  If  any  body  is  moved  through  a  distance  s  against  a  constant  force  F, 
how  much  work  is  done  ?  Give  proof.  In  what  direction  must  s  be  measured  ? 

A  body  whose  mass  is  9,800  grammes  is  raised  vertically  70  centimetres.  How 
much  work  is  done  ?  What  is  the  potential  energy  of  the  body  at  its  new  posi- 
tion as  compared  with  its  old  ?  Where  is  the  actual  energy  to  which  this  so- 
called  "  potential  energy  "  corresponds  ?  If  a  body  is  moving  with  accelerated 
motion,  what  should  we  mean  by  saying  that  it  was  accumulating  or  storing 
up  energy  ?  If  a  body  falls  freely  through  10  feet  in  one  case,  and  in  another 
descends  only  very  slowly  and  uniformly  through  the  same  distance,  does  it 
take  up  from  the  energy  of  gravitation  the  same  amount  of  energy  in  each 
case  ?  Does  "•  gravity  "  do  the  same  amount  of  work  in  each  case  ?  What  be- 
comes of  the  energy  in  each  case  ? 

Suppose  that  instead  of  falling  freely  the  same  body  falls  with  accelerated  mo- 
tion but  at  a  less  rate  than  if  free,  how  much  work  is  done  by  gravity  ?  How 
much  of  the  energy  remains  in  the  body  ?  What  becomes  of  the  remainder  ? 


OTHER  CONVENIENT  UNITS  OF  FORCE,  ENERGY, 
AND  WORK. 

British  Engineering  Units. — The  C.  G.  S.  system  of 
units  is  almost  universally  employed  in  modern  scientific 
work  ;  but  for  engineering  and  commercial  purposes  several 
other  systems  are  in  common  use,  partly  for  convenience, 
and  partly  from'  the  continuance  of  long-established  custom. 
The  units  of  these  various  systems  differ  in  no  other  respect 
than  in  magnitude. 

The  British  engineering  unit  of  length  is  the  foot  (one 
third  of  the  standard  yard)  ;  the  unit  of  time  is  the  second 
in  general,  but  frequently  the  minute  or  hour,  in  dealing 
with  long  times ;  the  unit  of  force  is  the  weight  of  one 
pound — i.  e.,  the  force  with  which  the  quantity  of  matter 
called  the  standard  pound  is  attracted  to  the  earth. 

British  Engineering  Unit  of  Mass. — Having  thus 
defined  the  unit  of  force,  we  must  next  deduce  the  unit  of 
mass.  By  definition  (page  90),  the  unit  force  is  a  force 
which  will  produce  a  unit  acceleration  in  a  unit  mass.  In 
the  British  engineering  system,  a  force  equal  to  the  weight 
of  one  pound  would  produce  an  acceleration  of  one  foot  per 
second  when  acting  upon  a  unit  mass.  Let  a  mass  of  one 


B.  E.   UNITS.  99 

pound  fall  freely.  The  force  accelerating  it  is  the  weight 
of  one  pound.  The  mass  accelerated  is  the  pound  mass. 
What  acceleration  is  produced?  Exact  experiments  show 
that  the  acceleration  will  be  very  nearly  32'2  feet  per  second. 
The  acceleration,  then,  is  32'2  times  what  the  unit  of  force 
would  produce  in  the  unit  of  mass.  Hence  the  mass  of  one 
pound  is  only  $%.%  part  of  a  unit  of  mass,  and  the  Unit  of 
Mass  in  the  British  Engineering  (B.  E.)  System  must  be  the 
mass  of  32-2  pounds — i.  e.,  82-2  times  the  mass  contained 
in  the  standard  pound.  This  unit  has  no  special  name. 

If,  then,  we  find  by  the  balance  that  an  object  contains 
a  certain  number  of  pounds  of  matter — e.  g.,  80-5  pounds — 
then  its  mass  expressed  in  B.  E.  units  of  mass  would  be 
80-5  -r-  32-2  =  2-5  units. 

Therefore,  to  find  the  number  of  B.  E.  units  of  mass  in 
an  object,  ascertain  by  the  balance  the  number  of  pounds 
mass  it  contains  and  divide  by  32-2. 

The  B.  E.  unit  of  mass  is  simply  a  larger  mass  than  the  mass  of 
the  standard  pound,  just  as  the  foot  is  a  larger  unit  of  length  than  the 
inch.  As,  then,  we  can  express  a  distance  of  54  inches  by  calling  it 
54  H-  12  =  4*5  feet,  so  we  can  express  a  mass  of  70  pounds  by  calling 
it  70  •*•  32-2  =  2-17  B.  E.  units  of  mass. 

The  B.  E.  Unit  of  Work  is  the  foot-pound— that  is, 
the  work  done  in  moving  an  object  through  a  distance  of 
one  foot  by  or  against  a  force  of  one  pound. 

If  a  horse  pulls  a  wagon  100  feet  with  a  constant  force  of  75 
pounds,  how  much  work  in  B.  E.  units  does  he  perform?  W=  Fs  = 
75  x  100  =  7,500  foot-pounds. 

The  B.  E.  Unit  of  Energy  is,  of  course,  the  same  as 
that  of  work,  viz.,  the  foot-pound,  as  the  amount  of  work  is 
merely  the  amount  of  energy  transferred  or  transformed. 

EXAMPLES. — How  much  energy  would  a  ton  acquire  in  falling 
through  5  feet  ?  E  —  W  =  Fs  =  2,000  x  5  =  10,000  foot-pounds.  Or  in 
falling  5  feet  it  would  acquire  a  velocity  (page  20)  such  that  F2  =  2as, 
and  a  =  32-2  feet  /.  72  =  2  x  32-2  x  5  =  322  feet  per  second.  .-.  E  = 

2  000 
k M  V*  -  $  x  — ^  x  322  =  10,000  foot-pounds. 

' 


100  MASS,  FORCE,  ENERGY,  AND  WORK. 

What  would  be  the  energy  of  onward  motion  of  a  locomotive 
weighing  30  tons,  if  moving  with  a  velocity  of  a  mile  a  minute  f    E  = 


M  =  =  1,863  B.  E.  units.      F  =  =  88'0  feet  per 

oa'6  OU 

second.  .'.  E  =  £  x  1,863  x  882  =  7,210,000  foot-pounds.  Therefore  the 
engine  must  give  out  7,210,000  foot-pounds  of  energy  ;  or,  in  other 
words,  must  have  done  upon  it  7,210,000  foot-pounds  of  work  (by 
brakes,  etc.)  before  it  can  stop.  This  would  be  equal  to  the  work  of  rais- 
ing 7,210,000  pounds,  or  3,605  tons,  one  foot  vertically  against  gravity, 
or  one  ton  3,605  feet  (about  three  fourths  of  a  mile)  —  or  to  the  energy 

O   f*(\K 

acquired  by  the  engine  itself  in  falling  freely  through    '       =  120  feet. 

These  results  may  give  you  a  rough  idea  of  the  enormous  energy  of 
two  trains  coming  into  collision  at  high  speed.  But  think  how  small 
this  is  compared  with  the  energy  of  the  earth  moving  in  its  orbit  ! 

The  French  or  Metric  Engineering  System  is  based 
on  the  metre,  second,  and  kilogramme,  instead  of  on  the 
foot,  second,  and  pound  (see  page  540). 

The  various  units  of  mass,  force,  and  energy,  are  related  as  follows 
for  a  place  where  g  =  981  centimetres  per  second  : 

Mass  of  1  kilogramme  =  2'205  x  mass  of  1  pound. 
Weight  of  1  pound  (avoirdupois)  =  445,000  dynes. 

11        "  1  kilogramme  =  981,000  dynes. 

"        "  1  kilogramme  =  weight  of  2'205  pounds. 
1  foot-pound  =  13,560,000  ergs. 
1  kilogrammetre  =  98,100,000  ergs. 
1  foot-pound  =  013825  kilogrammetre. 

Energy  of  other  kinds  than  onward  motion  and  potential  energy, 
viz.,  heat-energy,  energy  of  vibration,  electrical  energy,  etc.,  may  al- 
ways be  expressed  in  ergs,  foot-pounds,  or  any  chosen  unit,  and  for 
some  purposes  are  so  expressed.  Quantities  of  energy  expressed  in 
other  units  can  be  reduced  to  ergs  or  foot-pounds,  if  we  know  how 
many  of  the  special  units  are  equivalent  to  an  erg  or  a  foot-pound. 

QUESTIONS.—  On  what  account  are  the  C.  G.  S.  units  not  convenient  for  engineer- 
ing work  ?  What  is  engineering  work  ?  In  what  respect  do  other  units  differ 
from  these  ?  Is  a  unit  anything  but  an  arbitrarily  chosen  quantity  ?  Can 
quantities  of  the  same  thing  differ  except  in  amount  ?  Name  the  B.  E.  units  of 
length,  time,  and  force.  Why  should  the  B.  E.  unit  of  force  be  denned  for  a 
certain  locality  ?  What  is  the  unit  of  mass  in  the  B.  E.  system  ?  What  is  the 
standard  mass  ?  Show  how  the  unit  of  mass  is  deduced.  Having  given  the 
mass  of  a  body  expressed  in  pounds,  how  would  you  find  its  mass  expressed  in 
B.  E.  units  of  mass  ?  What  is  the  mass  in  B.  E.  units  of  the  air  in  the  car  of  a 


RATE  OP  WORK.— POWER.  101 

former  example  ?    What  is  the  mass  of  the  car  ?    With  how  much  force  does 
the  car  press  upon  the  rails  ? 

In  what  unit  must  distances  be  expressed  before  being  used  for  computation  in 
the  B.  E.  system  ?  Times  ?  Masses  ?  What  would  happen  if  you  neglected  to 
express  them  in  these  units  ?  What  is  the  B.  E.  unit  of  work  ?  Of  energy  ? 
How  much  is  the  least  work  in  B.  E.  units  necessary  to  be  done  to  lift  a  man 
whose  mass  is  150  pounds  from  the  bottom  to  the  top  of  the  Washington  Monu- 
ment ?  How  much  would  his  potential  energy  due  to  gravitation  be  increased 
by  that  elevation  ?  How  much  energy  of  onward  motion  would  a  man's  body 
possess  when  it  reached  the  earth  falling  from  that  height  if  not  resisted  by  the 
air  ?  What  would  be  ^he  energy  in  B.  E.  units  of  onward  motion  of  the  steam- 
car  of  a  former  problem  ?  How  much  work  in  B.  E.  units  must  be  done,  neg- 
lecting losses,  to  start  or  stop  the  car  ?  If  the  engine  pulled  with  a  constant 
force  upon  a  train  of  five  such  cars,  and  was  required  to  pull  for  one  fifth  of  a 
mile  before  it  could  bring  them  from  rest  into  motion  at  the  stated  speed,  with 
how  much  force,  B.  E.  units,  must  it  pull,  all  friction  and  air  resistance  being 
neglected  ?  How  much  work,  B.  E.  units,  must  the  engine  do  simply  to  get 
the  mass  of  this  tram  up  to  speed  regardless  of  resistance  ? 


RATE  OF  WORK.— ACTION  AND  REACTION. 

Power. — Attention  has  been  called  to  the  fact  that  the 
amount  of  work  in  any  given  case  is  the  same,  whether  the 
work  is  done  rapidly  or  slowly.  To  lift  a  ten-pound  weight 
5  feet  high  requires  50  foot-pounds  of  work,  whether  the 
action  occupies  a  fraction  of  a  second  *or  a  century.  But 
the  rate  at  which  work  is  done  in  the  two  cases  would  be 
very  different.  By  rate  of  work  (also  called  activity)  is 
meant  the  amount  of  work  done^?er  unit  of  time. 

The  term  POWER  is  used  to  denote  the  rate  at  which  a 
source  of  energy  is  capable  of  doing  work — i.  e.,  of  giving 
up  energy.  The  relation  between  power  and  work  is  the 
same  as  that  between  velocity  and  motion — power  being  rate 
of  work,  velocity  rate  of  motion,  both  rates  being  with  re- 
spect to  time. 

The  B.  E.  unit  of  power  is  the  Horse-power.  It  is  a 
rate  of  work  of  550  foot-pounds  per  second,  and  very  roughly 
represents  the  rate  at  which  a  horse  can  keep  up  continuous 
work.  Thus,  to  raise  a  body  weighing  550  pounds  in  one 
second  through  a  vertical  distance  of  one  foot  against  gravity, 
would  require  work  at  the  rate  of  one  horse-power.  This 


102  MASS,  FORCE,  ENERGY,  AND  WORK. 

is  an  arbitrary  and  not  altogether  convenient  unit,  but  it  is 
in  very  general  use.  Other  units  of  rate  of  work  are  em- 
ployed in  electrical  measurements. 

An  electric  motor  is  required  to  run  an  elevator ;  what  must  be  the 
nominal  horse-power  of  the  motor  f  To  answer  the  question,  we  must 
know  the  rate  at  which  work  must  be  done  upon  the  elevator.  Sup- 
pose, then,  that  the  elevator  is  required  to  rise  at  a  speed  of  30  feet 
per  minute,  when  the  total  load  is  2  tons,  including  the  weight  of  the 
elevator.  Then,  neglecting  friction,  the  rate  of  work  must  be  2  x  2,000 

30 
x  —  =  2,000  foot-pounds  per  second.     One  horse-power  is  550  foot- 

2  000 

pounds  per  second ;  therefore,  -£— -  =  3*64  horse-power  is  the  least 

5oO 

horse-power  of  motor  which  will  do  the  work.  In  practice,  a  motor 
of  twice  this  capacity  would  be  used,  because  the  work  required  to  be 
done  against  friction  is  usually  very  great. 

Action  and  Reaction. — We  have  seen  that  two  bodies, 
or  at  least  two  particles  of  matter,  are  necessary  to  the  exist- 
ence of  a  force,  and  that  each  possesses  a  tendency  to  accel- 
eration. When  we  deal  with  the  effect  of  the  force  upon  that 
one  of  the  bodies  with  which  we  happen  to  be  concerned, 
regardless  of  the  other,  we  speak  of  the  effect  as  the  action 
of  the  force.  If  we  consider  the  effect  of  the  force  upon 
the  other  body,  we  speak  of  it  as  the  reaction  of  the  force. 
Whenever,  then,  there  is  a  force,  there  must  evidently  be 
both  action  and  reaction.  This  and  some  other  facts  are 
expressed  by 

Newton's  Third  Law  of  Motion. — "  To  every  action 
there  is  always  an  equal  and  contrary  reaction ;  or,  action 
and  reaction  are  equal  and  opposite." 

Hold  a  book  in  your  hand.  The  book  and  the  earth  tend  to  ap- 
proach each  other — that  is,  there  is  a  force  of  attraction  between  them. 
The  action  of  this  force  is  the  tendency  of  the  book  to  be  accelerated 
toward  the  earth,  or  its  motion  if  it  is  allowed  to  fall.  The  reaction 
is  the  tendency  of  the  earth  to  be  accelerated  toward  the  book,  or  its 
motion  if  allowed  to  move.  Notice  that  the  direction  of  motion  of  the 
earth  and  book  would  be  toward  each  other — i.  e.,  exactly  opposite. 


ACTION  AND  REACTION.  103 

As  shown  on  page  92,  the  product  of  the  force  into  the 
time  for  which  it  acts,  is  equal  to  the  momentum  produced. 
In  the  case  of  action  and  reaction,  the  force  is  the  same 
on  both  bodies  concerned,  and  so  long  as  it  acts  it  affects 
both  bodies.  Hence  the  product  of  the  force  into  the  time 
must  be  equal  for  both,  and  the  momentum  generated  in  one 
must  be  equal  to  that  of  the  other.  That  is,  if  m^  and  vv  be 
the  mass  and  velocity  of  one  body,  and  w2  and  v^  those  of 
the  other,  then  m^v^m^v^.  This  is  true  of  all  cases  of 
action  and  reaction,  of  impact  of  elastic 'bodies,  of  attraction 
and  repulsion  of  all  kinds,  etc. 

The  rate  of  action  of  a  force  is  measured  by  the  product  Ma  when 
acceleration  occurs.  Reaction  would  be  measured  in  the  same  way. 

The  terms  action  and  reaction  are  often  applied,  though  incorrectly, 
to  counterbalancing  forces.  For  instance,  when  an  object  rests  upon  a 
table,  the  elasticity  of  the  table  is  called  into  play,  and  the  table  exerts 
an  upward  force  upon  the  object  equal  and'  opposite  to  its  weight.  But 
there  are  here  two  distinct  forces,  and  the  case  is  not  one  of  action  and 
reaction  of  a  single  force.  The  fact  that  a  man  can  not  lift  himself  by 
pulling  at  his  boot-straps  is  an  example  of  balanced  forces,  not  of  ac- 
tion and  reaction.  Would  a  huge  bellows  operated  in  the  stern  of  a 
sail-boat  produce  a  wind  that  would  move  the  boat  I  Why  ? 

QUESTIONS.— What  is  meant  by  rate  of  work  ?  Power  ?  Activity  ?  What  is  a 
horse-power  ?  Is  it  an  amount  of  energy  ?  Why  ?  How  does  an  amount  of 
work  differ  from  a  rate  of  work  ?  Can  a  force  exist  without  affecting  at  least 
two  bodies  or  particles  of  matter  ?  Is  force  a  tendency  of  one  body  to  ap- 
proach another,  or  of  two  bodies  to  approach  each  other  ?  What  is  the  dis- 
tinction between  action  and  reaction  ?  Are  they  the  effects  of  the  same  or  of 
different  forces  ?  Give  examples  of  them.  State  Newton's  third  law  of  motion. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

Give  an  accurate  explanation  of  the  process  of  freeing  a  coat  from  dust  by  beat- 
ing or  shaking  it. 

A  single  tenth  of  a  grain  of  musk,  with  but  slight  diminution  of  its  weight,  will 
diffuse  a  perceptible  odor  through  a  room  for  years.  How  does  this  illustrate 
divisibility  ? 

How  many  cubic  feet  of  water  will  be  raised  in  an  hour  from  a  well  50  feet  deep, 
if  the  rate  of  piimping  be  15  horse-power  ?  (Reckon  one  horse-power  as  equiv- 
alent to  8'8  cubic  feet  of  water  lifted  1  foot  high  per  second,  and  the  weight  of 
a  cubic  foot  of  water  at  6^^  pounds.)  ^ 

Prove  that  the  injuries  received  in  railway  accidents  are  largely  due  to  inertia. 


104  MASS,  FORCE,  ENERGY,  AND  WORK. 

The  tendency  of  the  ball  being  to  retain  the  velocity  imparted  to  it  in  the  can- 
non, what  takes  place  when  it  strikes  the  wall  of  a  fort  ?  Why  ? 

A  cannon-ball  weighing  500  pounds  is  shot  from  a  gun  weighing  20  tons.  What 
are  the  relative  momenta  ?  If  the  ball  leaves  the  gun  with  a  velocity  of  2,000 
feet  per  second,  what  is  the  velocity  of  recoil  of  the  gun  ?  Momentum  of  ball 

=  mi  «i=  jjj^g  *  2,000  =  31,000.    The  momentum  (m2  va)  of  the  gun  is  the  same 
Hence  its  verity  .  «£?.     Now,  „„  =  »g™  <£      t,  „  *«»»  ^ 
second.  1<J4U 

If  an  engine  is  raising  a  mass  of  20  tons  at  a  rate  of  2  feet  a  second,  how  many 
horse-power  is  the  engine  exerting  ?  Ans.  145. 

Suppose  a  buUet  weighing  one  ounce  and  moving  with  a  velocity  of  1,000  feet  a 
second  is  found  to  penetrate  2  inches  into  a  plank.  What  must  be  the  average 
amount  of  the  force  in  B.  E.  units  exerted  by  the  bullet  ?  We  must  first  find 
E.  One  ounce  =  ^  pound  :  therefore,  mass  of  bullet  in  B.  E.  units  =  T^  -*•  32'2  = 
0-00194  B.  E.  units.  E  =  £  x  '00194  x  10002  =  970  feet  per  pound.  Now  s  =  2  in  = 

A  ft.  =  J  ft.   /.  F  ^  -j-  =  —  =  5820  pounds. 

A  person  weighing  130  pounds  walks  up  a  flight  of  stairs  composed  of  45  steps, 
each  8  inches  high.  How  much  work  in  B.  E.  units  is  the  least  that  he  can  do  ? 
He  must  lift  himself  through  45  x  8  inches  =  30  feet.  He  must,  therefore,  do  W 
=  F  s  =  130  x  30  foot-pounds  of  work.  What  would  be  the  potential  energy  of 
the  person  when  half-way  up  ? 

A  body  is  found  by  the  balance  to  contain  150  pounds  of  matter.  What  is  its 
mass  in  B.  E.  units  ?  What  is  the  mass  of  your  body  ? 

What  is  the  mass  of  a  ton  of  coal  in  B.  E.  units  ? 

A  clock-weight  has  a  mass  of  2,000  grammes,  and  descends  in  a  day  through  a 
weight  of  10  centimetres.  How  much  work  is  done  upon  it  by  gravity  ?  W  = 
Fs(F  =  2,000x980  dynes).  Ans.  19,600,000  ergs. 

With  how  much  force  in  B.  E.  units  does  a  locomotive  weighing  30  tons  press 
upon  the  rails  ? 

We  may  make  use  of  the  cart  experiment  to  determine  the  number  of  dynes  in 
the  weight  of  a  gramme  mass.  Suppose  we  make  the  mass  in  W,  including  the 
pan,  100  grammes,  and  vary  the  mass  in  the  cart  until  it  moves  over  180  centi- 
metres in  3  seconds,  and  that  we  then  find  by  the  balance  that  the  whole  mass 
M  of  C  and  W  is  2.450  grammes.  What  is  the  amount  of  the  accelerating  force, 
viz.,  the  weight  of  100  grammes  ?  (F  =  M  a.)  Ans.  98,000  dynes.  How  many 
dynes  in  a  one-gramme  mass  ? 

Suppose  a  steamer  to  be  sailing  at  the  rate  of  12  miles  an  hour,  and  a  ring  to  be 
tossed  at  the  same  rate  of  speed  across  the  deck  in  a  direction  perpendicular  to 
the  course  of  the  vessel ;  what  is  the  velocity  of  the  ring  relatively  to  the  sur- 
face of  the  sea  ? 

Why  does  a  base-ball  player,  in  catching  a  flying  ball,  allow  his  hand,  the  instant 
the  ball  touches  it,  to  be  carried  backward  in  the  direction  in  which  the  ball 
was  moving  ? 

Explain  the  recoil  of  a  gun  against  the  shoulder. 


DYNAMICS.  105 


ACTION   OF  FORCES. 

COMPOSITION,   EQUILIBRIUM,   AND    RESOLUTION    OF 
FORCES. 

Dynamics. — That  branch  of  Physics  which  investigates 
the  action  of  force  and  energy  is  called  Dynam'ics  (from  a 
Greek  verb  meaning  to  be  able).  That  part  of  Dynamics 
which  deals  with  balanced  forces  is  known  as  Stat'ics  (from 
a  Greek  verb  meaning  to  cause  to  stand) ;  that  part  which 
treats  of  motion  as  produced  by  force,  we  call  Kinet'ics. 
The  sections  on  Energy  and  Force,  which  you  have  already 
studied,  relate  to  Dynamics. 

Composition  of  Forces. — Force,  being  a  tendency  to 
acceleration,  and  being  measured  oy  the  acceleration  pro- 
duced on  unit  mass  (P=  Ma,  page  91),  may  be  represented 
by  lines,  in  the  same  manner  as  velocities  and  motion. 

Let  A  B,  Fig.  23,  represent  in  magnitude  and  direction  the  accel- 
eration which  a  given  force  F  would  produce  on  a  free  unit  mass ;  then 
A  B  also  represents  in  magnitude  and  direction  the  force  F  itself,  for 
this  acceleration  is  equal  to,  and  in  the  direction  of,  the  force. 

Suppose  a  second  force,  Fa,  to  act  simultaneously  with  Fj  on  a  free 
unit  mass,  and  that  A  C  represents  the 

magnitude  and  direction  of  the  accelera-  / "Z-"^' 

tion  produced  by  F2  alone.  Then  A  C 
represents  F2.  The  resultant  accelera- 
tion would  be,  as  shown  on  page  24, 
the  diagonal  A  D  of  the  parallelogram  ;  _, 

and    this    acceleration   is    that   which 

would  be  produced  by  a  single  constant  force  acting  in  the  direction 
A  D,  and  represented  in  magnitude  by  the  length  of  A  D.  The  free 
body  at  A  acted  upon  simultaneously  by  the  two  forces  FI  and  F3  (A  B 
and  A  C)  would  move  precisely  as  if  acted  upon  by  the  single  force  R, 
equal  to,  and  in  the  direction  of,  A  D. 

The  equivalent  single  force  found  in  this  way  is  called 
the  Resultant  Force,  or  simply  the  Resultant. 


106 


ACTION  OF  FORCES. 


EXAMPLE. — Two  constant  forces,  FI=  3  pounds  and  F2=  2  pounds, 
act  simultaneously  on  a  body  at  an  angle  of  60°  with  each  other. 
What  is  their  resultant  I  Draw  the  straight  line  A  B  (Fig.  23)  of  a 
length  3  units  (take  three  quarters  of  an  inch)  to  represent  Jf\. 
Through  A  draw  A  C  of  a  length  2  units  (two  quarters  of  an  inch), 
and  at  an  angle  of  60°  with  A  B,  to  represent  F*.  Complete  the  par- 
allelogram A  B  D  C.  Draw  the  diagonal  A  D.  Measure  its  length. 
You  will  find  it  to  be  3f6  quarters  of  an  inch  long.  Then  the  com- 
bined action  of  Ft  and  F*  is  equivalent  to  that  of  the  resultant  R  = 
AD  =  3*6  pounds  acting  relatively  to  F!  and  F2  in  the  direction  A  D. 

Equilibrium  of  Forces. — The  principle  of  the  com- 
position of  forces  shows  that  any  number  of  forces  acting 
simultaneously  at  a  point  are  equivalent  to  a  single  resultant 
force.  It  has  also  been  shown  (page  48)  that  to  counterbal- 
ance a  single  force — that  is,  to  prevent  acceleration — we  must 
apply  an  equal  and  opposite  force.  Therefore,  to  counter- 
balance a  set  of  two  or  more  forces,  acting  at  one  point, 
there  must  be  applied  at  that  point  a  force  equal  and  oppo- 
site to  the  resultant  of  the  set. 

Drive  smooth  wire  nails  into  an  upright  board  at  B  and  C.  Put 
upon  them  spools,  or,  better,  large  metallic  or  wooden  pulleys.  Knot 
together  firmly  three  cords  at  A.  Hang 
one  cord  over  the  pulley  B,  another  over 
C,  and  let  the  third  carry  the  weight  D. 
Upon  D  suspend  a  weight  of  5  pounds, 
on  C  a  weight  of  2-5  pounds,  and  on  B  a 
weight  of  4  pounds.  After  a  moment  the 
apparatus  will  come  to  rest.  A  little  jar- 
ring will  reduce  the  error  from  friction. 
Thore  will  then  be  three  forces  at  A  act- 
ing along  A  B,  A  C,  and  A  D  respectively. 
As  the  point  A  is  at  rest,  these  forces  are 
balanced,  or,  as  it  is  said,  are  in  Equilib- 
rium (from  Latin  words  meaning  equal 
balance). 

FIG.  24.-EQUIUBRITTM  oF  Let  US  see  how  the  forC6S  are  rel^ 

FORCES.  when  this  balance  occurs.     Put  up  behind 

A  a  large  sheet  of  paper  (or  the  apparatus 

may  be  used  in  front  of  a  blackboard).    Mark  on  the  paper  the  direc- 
tions of  the  cords  by  points  under  A,  E,  F,  and  G.    Take  away  the 


EQUILIBRIUM   OF  FORCES. 


107 


paper,  and  draw  lines  through  these  points,  and  you  will  have  lines 
A  E,  A  F,  A  G,  of  Fig.  24.  Select  any  two  of  these  forces,  say  F  and 
G.  Lay  off  along  A  F  a  distance  A  c  of  2'5  units  (in  Fig.  25  the  unit 
is  about  three  sixteenths  of  an  inch)  to  represent 
the  force  F.  Along  A  G  lay  off  a  distance  of 
A  d  of  5  units  to  represent  the  force  G.  Com- 
plete the  parallelogram  and  draw  the  diagonal 
A  /.  Measure  A  /  carefully,  and  you  will  find 
it  to  be  about  4  units — that  is,  the  resultant  of 
F  and  G  is  about  4  pounds  and  is  in  the  direc- 
tion A  /.  In  other  words,  the  two  forces,  act- 
ing in  the  lines  A  F  and  A  G,  are  equivalent  to 
a  single  force  of  about  4  pounds  acting  to  pull  A 
in  the  direction  A  /.  To  balance  this  single 
force  would  require,  according  to  our  previous 
statements,  another  force  equal  to  it  and  oppo- 
site in  direction.  Consult  the  data,  and  you  will 
see  that  the  third  force  E  is  almost  or  exactly 
4  pounds.  Observe  your  diagram,  and  not;e  that 
the  resultant  A  /  is  almost  or  exactly  in  the  same 
line  with  A  E,  but  in  the  opposite  direction. 

In  your  experiment,  then,  you  had  three  forces  in  equilibrium, 
and  you  have  shown  that  the  resultant  of  two  was  equal  and  oppo- 
site to  the  third.  If  you  had 
drawn  the  resultant  of  F  and  E, 
you  would  have  found  it  equal 
and  opposite  to  G,  and  so  on. 
The  previous  statements  have, 
therefore,  been  experimentally 
proved.  They  could  be  similarly 
demonstrated  for  several  forces 
by  using  more  pulleys,  as  in  Fig. 
26,  and  constructing  resultants 
(see  page  25).  The  student  is  ad- 
vised to  put  together  some  such 
simple  apparatus,  and  to  experi- 


FIG.  26.— RESULTANT  OF  SEVERAL 
FORCES. 


ment  for  himself. 


Resolution  of  Forces. — As  we  may  resolve  a  given  ac- 
celeration, velocity,  etc.,  into  components  in  any  specified 
directions,  so  we  may  by  the  same  methods  resolve  a  force 
ito  components — that  is,  we  may  find  by  rules  similar  to 


108 


ACTION   OF  FORCES. 


those  given  oil  page  26  the  forces,  in  two  or  more  specified 
directions,  which  would  be  equivalent  to  the  given  force. 

Resultant  of  Parallel  Forces. — Procure  two  spring- 
balances  reading  up  to  10  or  15  pounds ;  also  a  wooden  rod, 
C  D,  five  feet  long  and  about  seven  eighths  inch  square. 
Drive  two  nails,  E  and  F,  three  feet  apart  and  at  nearly 
equal  heights,  Hang  the  balances  at  A  and  B,  from  E  and 
F,  by  cords  whose  lengths  can  be  readily  changed  to  make 
up  for  the  stretch  of  the  springs.  To  determine  the  result- 
ant of  parallel  forces  in  the  same  and  opposite  directions, 
you  may  perform  the  following  experiments : 

Fasten  the  balances  to  the  points  G  and  H  of  the  rod  exactly  3 
feet  apart  and  about  one  foot  from  each  end.  Adjust  the  cords  until 
C  D  is  horizontal,  and  read  the  balances.  This  reading,  which  will  be 

called  the  zero  reading,  is  to  be 

allowed  for  in  all  other  readings. 

Hang  a  weight  K  of  6  pounds  at 

L  just  1  foot  from  H,  and  there- 
fore 2  feet  from  G.  Adjust  the 

cord  until  C  D  is  again  horizontal 

(to  have  it  at  right  angles  to  the 

forces).    Read  A  and  B,  and  allow 

for  zero  readings.     The  pull  on 

A  will  be  found  to  be  about  2 

pounds,  that  on  B  about  4  pounds. 

As  the  system  is  at  rest,  we  have 

an  equilibrium  of  three   forces, 

viz.,  the  downward  weight  K  and 


L, 


G 


FlG.  27. — TO  ILLUSTRATE  RESULTANT   OF  PARALLEL  FORCES. 

the  upward  elastic  forces  exerted  by  A  and  B.     The  weight  of  the  bar 
does  not  affect  the  results,  as  it  is  allowed  for  in  zero  readings. 

Notice  three  facts :  First,  the  three  forces  are  parallel  and  in  the 
same  plane ;  second,  the  sum  of  the  forces  (2  +  4)  in  one  direction  (up- 


RESULTANTS  OF  PARALLEL  FORCES.  109 

ward)  is  equal  to  the  force  (6)  in  the  opposite  direction ;  and  third, 
the  force  A  is  to  the  force  B  as  the  distance  L  H  is  to  the  distance 
L  G — that  is,  the  forces  are  inversely  as  their  respective  perpendicular 
distances  from  the  opposite  force. 

Try  again,  using  1C  =12  pounds  and  making  L'  6  inches  from  G, 
so  that  L'  G  :  L'  H  =  1  :  5.  You  will  now  find,  on  making  C  D  hori- 
zontal that  A  reads  10  pounds  and  B  2  pounds.  A  +  B  =  10  +  2  =  12 
pounds,  the  same  as  K.  A  :  B  =  10  :  2  =  L'  H  :  L'  G,  and  the  forces 
are  parallel.  A  similar  result  would  be  found  if  the  downward  force 
were  applied  anywhere  between  the  two  upward  forces. 

If  you  put  the  weight  on  outside  of  G  or  H,  the  apparatus  will 
overturn  and  no  equilibrium  will  be  produced. 

When  there  is  Equilibrium,  the  resultant  of  any  two 
of  the  forces  must  be  equal  and  opposite  to  the  third. 
Let  us  first  consider  the  two  upward  forces.  Their  result- 
ant must  be  equal  and  opposite  to  the  downward  force. 
Therefore,  from  the  result  of  the  experiment,  we  may  say 
that— 

For  two  parallel  forces  in  the  same  direction,  the  result- 
ant is  in  the  same  direction  and  parallel,  is  in  the  same 
plane  as  the  components,  and  is  equal  to  their  sum.  Its  line 
of  action  is  nearer  the  larger  force,  and  its  perpendicular 
distance  from  the  lines  of  actions  of  the  two  forces  is  in- 
versely as  the  magnitudes  of  those  forces. 

Consider  the  upward  force  A  and  the  downward  force 
K.  The  resultant  of  these  must  be  equal  and  opposite  to  B. 
Note  that  B  is  equal  to  the  difference  of  K  and  A,  and  is 
outside  of  the  line  of  action  of  the  two  forces  on  the  side  of 
the  greater  force  K.  Hence — 

For  two  parallel  forces  in  opposite  directions,  the  result- 
ant is  in  the  direction  of  the  larger  force  and  is  parallel  to 
the  components  and  in  the  same  plane.  It  is  equal  to  their 
difference,  is  outside  of  the  two  forces,  and  on  the  side  of 
the  larger  force. 

Resolution  of  Parallel  Forces. — By  an  application 
of  the  rules  just  deduced  for  the  resultant  of  parallel 


HO  ACTION  OF  FORCES. 

forces,  we   may  resolve  a  given   force   into  parallel  com- 
ponents. 

To  illustrate  :  Suppose  two  men,  A  and  B,  to  be  carrying  between 
them,  on  a  board  6  feet  long,  a  rock  weighing  100  pounds.  The  rock 
is  2  feet  from  A.  How  much  weight  is  each  man  bearing  ?  The  load 
Wi  on  A  must  be  to  that  W2  on  B  inversely  as  their  distances  from 
the  rock— that  is,  Wi  :  W2  -  4  :  2.  Hence,  W1 :  W,  +  W2  =  4  :  6.  But 
Wi  +  Wa  must  be  100  pounds,  therefore  Wl  :  100  =  4  :  6  and  Wt  = 

^  =  66  6  pounds.     Wa  is  then  equal  to  100  -  66-6  =  33-3  pounds. 


QUESTIONS.— How  may  forces  be  represented  by  lines  ?  Represent  two  forces 
acting  at  a  point  A  an  1  at  an  angle  of  45°  to  each  other,  one  of  5  pounds,  the 
other  of  8  pounds.  How  much  would  be  the  resultant  of  these  two  forces  if 
acting  simultaneously,  and  what  would  be  its  direction  ? 

A  large  rock  is  to  be  moved  northward  ;  two  horses  are  attached  to  it,  one  of 
which,  A,  always  pulls  200  pounds,  the  other,  B,  300  pounds.  If  A  pulls  south 
and  B  north,  what  will  be  the  resultant  pull  and  in  what  direction  ?  If  A  pulls 
northeast  and  B  northwest,  what  will  be  the  amount  and  direction  of  the  re- 
sultant pull  ?  In  what  direction  must  both  pull  to  give  the  maximum  result- 
ant ?  How  much  will  that  be  ?  Could  they  pull  in  any  other  directions  so  as  to 
give  a  resultant  in  a  northerly  direction  ? 

Two  men  are  pulling  at  opposite  ends  of  a  rope,  fastened  in  which  is  a  spring-bal- 
ance ;  A  is  pulling  with  a  force  of  50  pounds.  How  hard  must  B  pull  to  prevent 
the  rope  from  going  toward  A  ?  How  much  will  the  spring-balance  read  ? 

Three  men,  A,  B,  and  C,  are  pulling  horizontally  on  ropes  knotted  at  one  point  as  in 
Fig.  24.  A  pulls  north  20  pounds,  B  southeast  50  pounds,  C  southwest  30  pounds. 
To  what  single  pull  would  these  three  simultaneously  applied  be  equivalent  ? 
In  what  direction  and  by  what  amount  should  C  pull  just  to  produce  equilib- 
rium against  the  joint  pulls  of  A  and  B  ?  In  what  direction  and  by  what 
amount  should  a  fourth  man  pull  just  to  neutralize  the  pulls  of  A,  B,  and  C  in 
the  first  case  ? 

A  man  fastens  the  cord  of  Fig.  24  to  a  stake  in  the  ground  at  C  and  another  at  B, 
and  pulls  at  D  horizontally  with  a  force  of  20  pounds,  the  knot  being  at  such  a 
point  that  A  C  is  northwest,  A  B  northeast,  and  A  D  south.  What  is  the  pull  in 
A  B  and  in  A  C  ? 

Draw  a  diagram  in  which  the  angle  BAG  will  be  very  large,  nearly  180°,  so  that 
A  is  nearly  in  line  with  B  and  C,  and  find  the  pull  in  each  for  a  pull  of  1  pound 
at  D.  (This  would  be  the  condition  of  things  in  a  stretched  line  with  a  weight 
hung  about  at  its  middle.)  Stretch  a  clothes-line  between  two  hooks  and  hang  a 
weight  upon  it  near  the  middle.  Is  the  pull  along  the  line  and  on  the  hooks 
greater  or  less  than  the  weight  hung  on  the  line  ?  As  the  line  is  more  nearly 
straight  with  the  same  weight,  is  the  lengthwise  pull  greater  or  less  ? 

Why  do  the  linemen  leave  a  considerable  sag  in  electric  light  and  telegraph 
wires  ?  Can  you  stretch  a  long  rope  perfectly  straight  horizontally  ?  Why  ? 

A  weight  of  50  pounds  rests  on  the  top  of  a  wooden  frame  shaped  like  a  letter  Y 
upside  down,  whose  arms  are  at  right  angles  with  each  other.  How  much 
pressure  is  transmitted  down  each  arm  ? 


MOMENT  OF   FORCE.  HI 

A.  man  wishes  to  draw  a  heavy  stone  toward  a  tree  by  means  of  a  long  rope 
with  a  much  greater  force  than  he  can  exert  by  a  direct  pull.  How  can  he 
do  so  ? 

In  the  apparatus  of  Fig.  27,  K  is  20  pounds  and  is  half-way  from  G  to  H.  What  is 
the  pull  upon  A  and  B  ?  If  it  is  one  sixth  of  the  way  from  H  to  G,  what  will  be 
the  pull  upon  A  and  B  ? 

State  the  rules  for  the  resultant  of  two  parallel  forces  in  the  same  direction  ;  in 
opposite  directions. 

A  bridge  weighs  100  tons,  and  its  weight  is  uniformly  distributed  throughout  its 
length.  H  ,w  much  does  it  press  down  on  each  abutment  ?  Neglecting  the 
weight  of  the  bridge,  suppose  an  engine  weighing  30  tons  is  on  the  middle  of  a 
bridge.  How  much  of  the  load  does  each  abutment  carry  ?  Suppose  the  en- 
gine is  one  third  of  the  way  from  one  end  of  the  bridge,  how  many  tons1  press- 
ure due  to  the  engine  are  there  on  each  abutment  ?  How  many  tons  due  to 
engine  and  weight  of  bridge  together  ? 

A  man  and  a  boy  have  to  carry  together  a  heavy  object  of  whose  weight  the 
man  can  carry  just  three  fourths  and  the  boy  one  fourth.  If  they  hang  it  on  a 
stick  between  them,  at  what  point  on  the  stick  must  it  be  fastened  ? 


MOMENT  OF  FORCE.— CENTRIFUGAL   TENDENCY. 

Arm  of  a  Force. — Moment. — Sometimes  an  object  is 
pivoted,  so  that  it  can  not  move  bodily  onward  with  respect 
to  what  it  is  attached  to,  but  can  only  revolve.  For  instance, 
a  wheel  can  turn  around  on  its  axle,  but  can  not 
leave  the  wagon.  A  force  applied  to  such  a  pivoted 
object  can  merely  accelerate  its  rotation  about  the 
pivot. 

Procure  a  wooden  rod  about  2  feet  long,  1  inch  wide,  and 
half  an  inch  thick.  Bore  a  smooth  hole  near  one  end,  A  (Fig. 
28),  and  put  through  it  an  easily-fitting  wire  nail  or  screw. 
Drive  this  into  a  block  standing  out  from  a  vertical  surface. 
At  B,  connect  a  spring  balance,*  as  shown  in  the  figure, 
fastening  its  top  by  a 

cord  to  a  nail,  as  at  D.          ,  0 

A   I    o 
Draw  up    the  balance 

cord  until  A  B  is  hori- 
zontal;   slide  E  along 
until   D  E   is  at   right       FIG.  28.— To  ILLUSTRATE  THE  ARM  OF  A  FORCE. 
angles  to  A  B,  and  read 

the  balance.     Call  this  its  zero  reading.     To  make  an  experiment, 
hang  a  weight  W,  of  5  pounds  half-way  from  the  pivot  0  to  the 


*  Instead  of  the  balance,  a  cord,  pulley,  and  weight,  as  in  Fig.  24,  may  be  used. 


112  ACTION  OF  FORCES. 

point  E.  Draw  up  the  cord  D  until  A  B  is  horizontal.  Read  the 
balance,  and  allow  for  the  zero  reading.  The  corrected  reading  will 
be  found  to  be  2-£  pounds  —  that  is,  just  one  half  W.  Call  the  force 
exerted  by  the  balance,  F  ;  then  we  have  two  forces,  F  and  W, 
acting  at  different  distances,  0  C  and  0  E,  from  the  axis,  these  dis- 
tances being  measured  at  right  angles  to  the  line  of  action  of  the 
forces.  We  have  seen  when  0  C  was  one  half  of  0  E  that  F  was  one 
half  of  W.  Make  0  C  one  third  of  0  E,  and  W  6  pounds.  Then  you 
will  find,  on  adjusting  and  correcting,  that  F  is  2  pounds,  or  £  W. 

Put  in  another  nail,  to  hang  the  balance  so  that  E  will  come  about 
half-way  along  the  rod.  Adjust  the  rod  horizontally,  and  take  the  zero 
reading  as  before.  Put  on  the  weight  W,  or  6  pounds,  near  the  end  of 
the  rod,  so  that  W  will  be  on  the  other  side  of  E  from  0,  and  so  that 
0  C  will  be  twice  0  E.  Then  you  will  find  F  to  be  12  pounds—  i.  e., 
twice  W. 

You  see,  then,  that  in  all  cases 


The  distance  0  C  or  0  E,  measured  from  the  axis  of  ro- 
tation perpendicularly  to  the  line  of  action  of  the  force,  is 
called  the  Arm  of  the  force,  or  sometimes  the  Lever  Arm. 
The  product  of  a  force  into  its  arm  is  called  the  Moment  of 
the  force.  Thus,  W  X  0  C  is  the  moment  of  the  force  W 
with  respect  to  the  axis  0,  and  F  X  0  E  is  the  moment  of  F. 
A  moment  is  said  to  be  right-handed  when  it  tends  to  pro- 
duce rotation  in  the  direction  of  that  of  the  hands  of  a 
clock,  and  left-handed  when  the  tendency  is  in  the  opposite 
direction.  Thus,  in  the  experiment,  the  moment  of  W  was 
always  right-handed  and  that  of  F  left-handed. 

Equilibrium  of  Moments.  —  We  see,  then,  that  in  each 
case  in  our  experiment  there  was  equilibrium  when  the  right- 
handed  moment  (WxO  C)  was  equal  to  the  left-handed 
moment  (FxOE). 

A  body  may  be  acted  upon  by  any  number  of  forces. 
Take  the  case  where  these  act  in  any  direction  whatever  in 
the  same  plane  or  in  parallel  planes.  They  will  be  in  equi- 
librium when  the  sum  of  the  right-handed  moments  is  equal 


COUPLES.  113 

to  that  of  the  left-handed  moments.  This  may  be  proved 
by  means  of  the  apparatus  numbered  5  in  the  illustration 
on  page  60. 

Couples. — If  two  equal  and  opposite  parallel  forces 
act  upon  a  body,  they  are  called  a  Couple.  We  have  shown 
that  the  resultant  of  two  parallel  forces  is  equal  to  their 
difference ;  when  the  forces  are  equal,  their  resultant,  there- 
fore, is  zero.  A  couple  does  not  tend  to  move  a  body  as  a 
whole. 

Let  FI  and  F2,  applied  at  the  points  a  and  &,  represent  a  couple. 
Draw  a  line  c  d  perpendicular  to  and  joining  the  lines  of  action  of  the 
two  forces.    Then  c  d  is  called  the  arm  of  the  couple.    The  moment 
of  the  couple  is  the  product  of  either  force 
into  the  arm  c  d — i.  e.,  moment  =  Fx  x  c  d 
=  F2  x  c  d. 

A  couple  can  not  be  counterbalanced 
by  any  single  force,  but  requires  the  appli- 
cation of  another  couple  opposite  in  direc- 
tion and  of  equal  moment  in  the  same  or 
a  parallel  plane.  FIG.  29. -A  COUPLE. 

Central  Force ;  Body  revolving  in  Circle. — Tie  a 

small  stone,  or  any  dense  object,  at  the  end  of  a  strong  cord 
two  or  three  feet  long.  Swing  the  stone  around  the  hand 
so  that  it  revolves,  at  a  nearly  uniform  speed,  in  a  circle,  as 
A  E  F  G,  Fig.  30.  You  will  notice  that  you  are  obliged  to 
exert  a  steady  pull  or  force  upon  the  cord  in  order  to  keep 
the  stone  from  flying  away  from  you.  The  cord  serves 
merely  to  transmit  this  force  from  your  hand  to  the  stone, 
thus  pulling  the  stone  continually  toward  the  hand. 

A  body  revolving  uniformly  in  a  circle  must  be  acted  on 
by  a  constant  force  toward  the  center  of  the  circle. 

While  the  stone  is  revolving,  let  go  or  cut  the  cord  at  any  instant. 
The  stone  will  fly  off  in  some  direction.  What  will  that  direction  be  1 
Try  the  experiment  several  times  by  swinging  the  stone  in  a  horizontal 
circle,  just  above  a  smooth  floor,  and  looking  down  upon  it  from  above. 
The  curved  path  due  to  gravity  will  thus  be  avoided.  Note  carefully 
the  direction  in  which  the  stone  flies  off  each  time.  You  will  see  that 


ACTION   OF  FORCES. 

this  is  the  direction  of  the  straight  line  tangent  to  the  circle  at  the 
point  at  which  the  stone  was  at  the  moment  of  release.  For  instance, 
if  it  were  at  A,  Fig.  30,  when  you  let  go  the  cord,  it  would  move  off 
along  the  straight  line  A  B  D,  tangent  at  A.  The 
tangent  is  the  direction  of  motion  of  the  stone  (page 
16)  at  that  instant.  It  is  evident  that  this  must  be 
the  case,  because,  after  you  release  the  cord,  the  stone 
moves  off  merely  by  virtue  of  its  inertia,  and  must, 
therefore,  follow  the  law  of  inertia  as  expressed  by 
Newton's  first  law  of  motion  (page  31).  If,  then,  the 
F  3Q  body  A  is  revolving  uniformly  in  the  circle  A  E  F  Gr 

with  such  a  velocity  that  it  would  pass  from  A  to  E 
along  the  circle  in  a  given  time,  it  would,  if  released  at  A,  pass  along 
the  straight  line  A  D  with  the  same  velocity,  reaching  a  point  B  such 
that  A  B  =  A  E  in  that  time. 

An  object  thus  revolving,  therefore,  tends  to  fly  off  at  a 
tangent,  and  with  the  same  velocity  that  it  is  moving  along 
its  path.  Every  point  beyond  A  of  the  tangent  A  B  D  is 
farther  from  the  center  than  the  circle  itself.  Hence  we 
may  say  that  the  object  tends  to  fly  away  from  the  center ; 
but  notice  that  it  does  not  tend  to  fly  off  radially.  This 
tendency  may  be  called  the  Centrifugal  (flying  from  the 
center)  Tendency.  The  force  required  to  keep  the  body  in 
its  circular  path  is  called  the  Centripetal  (center -seeking)  or 
Central  Force. 

Give  the  cord  a  certain  length,  perhaps  six  inches.  Whirl 
the  stone  twice  a  second.  Notice  the  pull  (central  force) 
which  you  give.  Then  whirl  the  stone  twice  as  fast — that 
is,  four  times  a  second.  Notice  that  the  central  force  re- 
quired is  much  greater.  In  fact,  with  double  the  number 
of  turns,  the  force  required  is  four  times  as  great ;  with 
treble  the  number,  nine  times,  etc.  The  central  force  is, 
therefore,  proportional  to  the  square  of  the  number  of  turns 
per  unit  of  time,  the  radius  remaining  the  same. 

Now  make  the  radius  twice  as  great  and  turn,  as  at  first, 
twice  a  second.  The  central  force  required  will  be  twice 
as  great.  If  the  radius  be  made  three  times  as  great,  the 


CENTRAL  FORCE.  115 

force  will  be  three  times  that  exerted  at  first.  The  central 
force  is,  therefore,  directly  proportional  to  the  radius  of  the 
circle,  the  number  of  turns  remaining  the  same. 

Compare  the  pull  required  for  two  stones,  one  of  twice 
the  mass  of  the  other,  but  whirled  in  circles  of  equal  radii 
and  at  the  same  rate.  The  central  force  will  be  found  pro- 
portional to  the  mass. 

The  velocity  of  the  body  in  the  orbit  being  uniform,  the  central 
force  is  doing  no  work.  Its  effect  is  merely  continually  to  change  the 
direction  of  motion  of  the  body.  The  centrifugal  tendency  of  the  body 
is  erroneously  called  "  centrifugal  force."  It  is  not,  however,  a  force 
at  all.  The  only  force  exerted  is  the  centripetal  or  central  force,  which 
is  of  such  an  amount  as  to  change  the  direction  of  the  momentum  just 
fast  enough  to  keep  the  body  moving  in  the  circle. 

When  you  are  whirling  a  stone  in  a  vertical  circle,  you  will  notice 
that  the  pull  is  greater  'when  the  stone  is  at  the  bottom  of  its  path 
and  less  when  it  is  at  the  top.  This  is  because  at  the  bottom  you  have 
to  exert  the  central  force  plus  the  weight  of  the  stone,  and  at  the  top 
only  the  central  force  minus  the  weight.  If  the  stone  is  revolving  at 
such  a  rate  that  the  central  force  is  less  than  the  weight,  then  it  will 
not  rise  to  the  top  of  the  circle,  but  will  go  up  part  way  and  fall,  as 
you  can  see  by  making  the  stone  whirl  fast  and  then  allowing  it  to 
slow  down  by  the  resistance  of  the  air. 

Every  Revolving  Object  affords  an  Example  of 
Central  Force  and  centrifugal  tendency.  The  grandest 
illustration  to  be  found  is  in  the  motions  of  astronomical 
bodies.  The  moon  revolves  around  the  earth  in  a  nearly 
circular  orbit,  and  is  held  in  that  orbit  by  a  central  force, 
which  we  are  next  to  study  under  Gravitation.  Similarly,  the 
earth  and  all  the  planets  revolve  in  orbits  about  the  sun,  the 
central  force  again  being  gravitation.  If  gravitation  were 
to  cease,  all  the  heavenly  bodies  would  move  off  in  straight 
lines,  and  the  entire  order  of  the  universe  would  be  changed. 

As  the  earth,  a  wheel,  or  any  object,  revolves  upon  its 
axis,  every  particle  of  matter  in  it  tends  to  fly  off  at  a  tan- 
gent. To  prevent  this  motion,  some  force — cohesion,  gravi- 
tation, etc. — must  be  exerted.  You  know  how  mud  flies  from 


116 


ACTION  OF  FORCES. 


a  rapidly  turning  carriage-wheel.  This  is  because  the  force 
of  adhesion  of  the  drops  to  the  wheel  is  not  great  enough 
to  overcome  the  centrifugal  tendency,  or,  in  other  words,  to 
change  the  direction  of  the  momentum  of  the  drops  fast 
enough  to  keep  them  against  the  surface  of  the  wheel. 

Objects  resting  upon  the  surface  of  the  earth  are  held  in 
place  by  their  weight,  although,  owing  to. the  revolution  of 
the  earth  upon  its  axis,  they  have  a  centrifugal  tendency. 
But  if  the  earth  were  to  revolve  about  seventeen  times  as 
fast  as  it  now  does,  objects  at  the  equator  would  have  a  cen- 
trifugal tendency  equal  to  their  weight,  and  would  fly  off  at 
a  tangent. 

A  grindstone,  revolving  rapidly,  throws  off  water  from  its  wet  sur- 
face for  a  similar  reason.  If  the  stone  be  revolving  very  fast,  the 
centrifugal  tendency  of  its  outer  portion  may  become  greater  than  its 
cohesion  can  withstand,  so  that  it  will  fly  asunder,  its  parts  moving  off 
with  great  energy.  Large  stones  bursting  in  this  way  may  do  much 
damage ;  and  heavy  fly-wheels  of  engines,  or  other  parts  of  machinery 
which  revolve  at  high  speed,  must  be  carefully  designed,  so  that  they 
may  be  strong  enough  to  resist  the  centrifugal  tendency. 

EXPERIMENTS. — Suspend  a  tumbler  by  a  stout  cord  tied  about  it  so 
that  it  will  hang  upright.  Partly  fill  it  with  water.  Twist  the  cord 

around  several  times  and  then  let 
it  untwist,  twirling  the  tumbler. 
Notice  how  the  water  moves  out- 
ward, piling  up  at  the  side  of  the 
tumbler,  and  even  flying  out  over 
the  edges  if  the  twirling  is  fast 
enough.  What  does  this  illustrate  ? 
Whirl  the  apparatus  shown  in 
Fig.  31.  Notice  how  the  hoops 
bulge  at  the  equator,  being  drawn  in 
at  the  poles.  How  is  this  owing  to 
centrifugal  tendency  ?  Why  is  the 
action  more  pronounced  at  higher 

SP*M  What  Preven'S  'he,  h°°PS 
from  flattening  out  entirely?  sup- 
pose the  earth  were  slightly  fluid  or  pasty,  and  were  revolving  on 
its  axis  as  it  now  does,  what  form  would  it  take?  Why?  The  earth 


CENTRIFUGAL  TENDENCY. 

actually  has  such  a  form,  and  doubtless  from  the  action  of  this  cause 
when  it  was  in  a  less  rigid  condition  than  no\y.  Why  is  the  centrifu- 
gal tendency  greater  at  the  earth's  equator  than  at  the  poles'? 

This  fact  enables  us  to  account  for  the  difference  of  weight  of  a 
given  body  at  various  parts  of  the  earth's  surface.  At  the  equator,  the 
body  has  the  greatest  centrifugal  tendency,  and  is  also  farthest  from 
the  earth's  center ;  its  weight  from  both  of  these  causes  is  less  than 
elsewhere  on  the  earth.  At  the  poles  it  would  be  nearest  to  the  center 
and  would  have  the  least  (in  fact  no)  centrifugal  tendency.  Its 
weight  would,  therefore,  here  be  the  greatest.  At  intermediate  lati- 
tudes, the  weight  would  be  between  these  two  extremes. 

When  a  railroad  train  is  going  round  a  curve,  the  centrifugal  tend- 
ency must  in  some  way  be  neutralized.  To  do  this,  the  outer  rail  is 
raised  higher  than  the  inner  one.  The  weight  of  the  cars  (acting 
through  their  center  of  mass)  may  then  be  resolved  into  two  compo- 
nents, one  perpendicular  to  the  inclined  bed  of  the  track  and  simply 
pressing  the  train  against  the  track,  the  other  horizontal  and  toward 
the  inside  of  the  curve.  '  The  latter  will  then  give  the  necessary  cen- 
tral force.  The  tangential  component  will  differ  in  amount  with  the 
speed  of  the  car,  so  the  track  can  not  be  laid  to  suit  all  speeds ;  it  is 
designed  only  for  the  greatest  speeds.  You  will,  therefore,  not  feel  the 
tipping  on  the  curve  in  a  fast-running  train,  while  you  will  notice  it 
on  the  same  curve  in  a  slow  train.  Why  does  a  bicycle-rider,  in  going 
rapidly  round  a  curve,  lean  toward  the  inside  of  the  curve? 

QUESTIONS. — If,  in  the  apparatus  of  Fig.  28,  W  is  made  10  pounds,  and  is  one  fifth 
of  the  way  from  O  to  E,  what  will  the  balance  read  ?  Reverse  the  positions  of 
balance  and  W,  and  what  will  the  former  read  ? 

What  is  meant  by  the  moment  of  a  force  ?    By  the  arm  of  a  force  ? 

A  force  of  6  pounds  acts  on  a  pivoted  body  at  such  a  point  that  the  perpendicular 
distance  from  the  pivot  to  the  line  of  action  of  the  force  is  3  feet ;  what  is  the 
moment  of  the  force  ?  What  is  meant  by  right-handed  and  left-handed  mo- 
ment ?  Suppose  the  moment  in  the  preceding  problem  were  right-handed, 
how  much  would  be  the  magnitude  of  the  moment  required  to  counterbalance 
it  ?  What  must  be  its  direction  ?  If  its  arm  were  9  feet,  what  must  be  the 
amount  of  the  force  ?  Draw  various  diagrams  representing  a  pair  of  forces 
whose  moments  are  counterbalanced. 

A  boy  weighing  50  pounds  sits  on  one  end  of  a  board  placed  across  a  log,  and 
another  boy  weighing  100  pounds  sits  on  the  other  part  of  the  board  ;  how  far 
out  from  the  log  must  the  second  boy  sit  to  balance  the  first  ?  How  much  will 
be  the  downward  pressure  upon  the  log  ? 

The  forces  of  a  couple  are  20  pounds  each,  and  their  perpendicular  distance  apart 
is  4  feet,  what  is  the  moment  of  the  couple  ?  Define  a  couple. 

What  kind  of  a  force  is  necessary  to  keep  an  object  revolving  uniformly  in  a 
circle  ?  In  what  direction  does  such  an  object  tend  to  fly  off  if  that  force  ceases  ? 
Why  ?  Why  may  this  tendency  be  called  a  centrifugal  tendency  ?  Why  is  it 


ACTION  OF  FORCES. 

better  called  a  tangential  tendency  ?  Why  should  it  not  be  called  a  centrifugal 
force  ?  What  is  meant  by  central  force  ?  By  centripetal  force  ?  What  does 
this  force  do  ?  Does  it  perform  any  work  on  an  object  revolving  in  a  circular 
orbit?  Why? 


MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

Why  does  the  weight  of  a  body  differ  at  different  points  of  the  earth's  surface  ? 
If  a  standard  pound-weight  and  a  weighed  pound  of  shot  were  exactly  bal- 
anced at  Chicago,  would  they  cease  to  balance  each  other  if  transferred  to 
Quito  ?  If  you  should  buy  a  quantity  of  nails  in  the  city  of  Mexico  that  would 
weigh  exactly  a  pound  on  a  spring-balance,  would  they  weigh  more  or  less 
than  a  pound  on  the  same  balance  at  Hammertest  in  Norway  ?  Why  ? 

Construct  a  diagram  showing  what  must  be  the  direction  followed  by  a  barge 
drawn  by  two  horses  on  opposite  sides  of  a  canal. 

Illustrate  in  a  similar  manner  the  resultant  in  the  case  of  the  onward  motion  of 
a  swimmer  striking  the  water  with  both  hands  ;  the  darting  of  a  trout  in  a 
straight  line  by  the  action  of  two  pectoral  fins. 

Of  what  tendency  is  advantage  taken  in  discharging  a  stone  from  a  sling  ?  Have 
you  read  of  instances  in  history  where  sufficient  velocity  was  in  this  way  com- 
municated to  projectiles  to  render  the  sling  a  formidable  weapon  ? 

Why  are  cushions  and  hair  mattresses  soft  and  comfortable  ?  On  what  does  the 
action  of  carriage-springs  depend  ? 

There  is  a  legend  that  in  an  exhibition  of  skill  Richard  the  Lion-hearted  severed 
an  iron  bar  with  his  sword,  while  Saladin  surprised  his  opponent  by  cutting  a 
feather  pillow  in  halves  with  his  scimiter.  Explain  the  principles  which  made 
these  feats  possible. 

Have  you  ever  seen  the  animals  in  a  cattle-train  thrown  violently  off  their  feet 
when  the  cars  are  suddenly  stopped  ?  Why  is  this  ? 

In  accordance  with  what  principle  do  athletes  make  longer  running-  than  stand- 
ing-jumps ? 

On  the  top  of  one  of  the  fingers  of  your  left  hand,  balance  a  card  with  a  penny 
placed  upon  it ;  strike  the  card  suddenly  with  the  middle  finger  of  the  right 
hand,  when  it  will  fly  away  and  the  penny  remain  on  the  finger.  Why  ? 

Suppose  that  a  leader  of  silk-worm  gut  will  just  pull  out  a  spring-balance  to  the 
6-pound  notch  without  breaking.  How  much  strain  will  it  bear  from  the  angler 
and  from  the  salmon  when  they  are  pulling  at  cross-purposes  ? 

Why  does  a  gunner  follow  flying  game  with  his  piece  before  firing  ? 

Each  of  the  chain  of  bones  forming  your  spine  is  separated  from  its  neighbors  by 
disks  of  elastic  tissue.  What  happens,  then,  when  you  jump  heavily  on  your 
feet  from  a  height  ?  Is  the  brain  seriously  jarred  ?  Can  you  think  of  a  reason 
why  a  man  is  a  little  taller  in  the  morning  than  at  night  ?  Why  you  should  not 
form  the  habit  of  sleeping  on  a  high  pillow  ? 

Enumerate  all  the  forces  acting  upon  a  ball  thrown  into  the  air.  As  its  velocity 
diminishes,  what  is  its  direction  ?  Why  is  it  found  necessary  to  elevate  a  rifle 
in  order  that  the  bullet  may  strike  a  distant  target  ? 

May  gravity  be  nullified  by  the  centrifugal  tendency  ? 

If  a  stick  10  feet  long  is  supported  at  a  point  3  feet  from  one  end,  what  weight 
hung  from  this  end  will  be  supported  by  12  pounds  hung  from  the  other  ? 

Have  you  ever  seen  two  buckets  evenly  balanced  in  a  well  at  opposite  ends  of  a 
rope  ?  Explain  this  as  a  simple  example  of  equilibrium  of  forces. 


FORCE  OF   GRAVITATION.  119 

Suppose  a  vessel  steaming  at  the  rate  of  12  miles  an  hour  to  be  ascending  a  river 
the  velocity  of  whose  current  is  2J  miles  an  hour  ;  at  what  rate  will  it  progress  ? 
What  will  be  its  speed  in  descending  the  same  river  ? 

A  locomotive  weighing  20  tons  moves  with  a  velocity  of  40  feet  a  second.  Another 
locomotive  weighing  25  tons  moves  at  the  rate  of  4,800  feet  in  a  minute.  How 
do  their  velocities  compare  ?  How  do  they  compare  in  momentum  ? 

If  the  wind  is  blowing  southwest  with  a  velocity  of  10  miles  an  hour,  what  are  the 
southerly  and  westerly  components  ?  Ans.  7'07  each. 

Assume  that  two  hunters  are  canying  a  deer  suspended  from  a  pole  resting  on 
their  shoulders.  What  is  the  proportion  which  each  bears— 

1.  When  the  deer  is  half-way  between  them  ? 

2.  When  its  distance  from  the  first  is  four  times  its  distance  from  the  second  ? 


GRAVITATION  AND  THE  PENDULUM. 

UNI  VERSAL   GRA  VITA  TION. 

Every  Particle  of  Matter  tends  to  approach  every 
other  Particle ;  or,  in  other  words,  any  two  particles  of 
matter  whatever  will  be  accelerated  toward  each  other  un- 
less such  motion  is  prevented.  There  appears,  therefore,  to 
be  some  form  of  energy  which  causes  a  universal  force  of 
attraction.  This  force  is  called  Universal  Gravitation.  The 
nature  of  the  energy  causing  it  is  unknown.  The  law 
which  expresses  the  action  of  the  force  of  gravitation  was 
first  stated  by  Newton,  and  is  as  follows  : 

1.  Every  particle  of  matter  in  the  universe  attracts  every 
other  particle. 

2.  The  direction  of  the  force  between  any  two  particles 
is  that  of  the  straight  line  joining  them. 

3.  The  magnitude  of  the  force  is  directly  proportional  to 
the  product  of  the  masses  of  the  two  particles,  and  inversely 
proportional  to  the  square  of  their  distance  apart. 

A  Homogeneous  Spherical  Body,  with  reference  to 
any  body  outside  itself,  acts  as  if  all  its  mass  were  concen- 
trated at  its  center.  Thus,  two  spheres  of  uniform  material 
attract  each  other  with  a  force  proportional  to  the  product 


120  GRAVITATION  AND  THE   PENDULUM. 

of  their  masses  divided  by  the  squares  of  the  distance  be- 
tween their  centers. 

Gravitation    appears    to    act   Instantaneously. — 

There  is  reason  to  suppose  that  if  a  new  mass  of  matter 
could  be  created  suddenly  in  space,  its  attraction  would  be 
felt  in  an  imperceptibly  short  time  on  every  existing  particle 
of  matter,  at  least  within  the  limits  of  the  visible  universe. 

Gravitation  between  two  Bodies  is  not  affected 
by  interposing  any  other  Body. — When  the  moon,  for 
instance,  passes  into  the  shadow  of  the  earth  and  is  eclipsed, 
the  earth  is  directly  between  the  moon  and  the  sun ;  but  the 
attraction  between  the  moon  and  sun  is  apparently  not  in 
the  least  diminished  or  increased  in  consequence.  A  body 
weighed  in  the  air  shows  no  apparent  change  in  weight  by 
placing  other  objects  between  it  and  the  earth,  the  very 
minute  increase  due  to  the  attraction  between  such  objects 
and  the  body  being  imperceptible. 

The  energy  which  produces  universal  gravitation  is  the  source  of 
the  immense  forces  necessary  to  keep  the  planets  in  their  orbits  around 
the  sun,  and,  indeed,  to  hold  together  the  whole  astronomical  system. 
Some  idea  of  the  amount  of  the  force  of  attraction  due  to  gravitation 
may  be  obtained  from  the  statement  that  two  homogeneous  spheres, 
each  having  the  mass  of  one  ton  and  at  a  distance  of  10  feet  between 
centers,  would  attract  each  other  with  a  force  of  only  a  little  more  than 
a  millionth  of  the  weight  of  a  pound ;  whereas,  the  force  of  attraction 
between  the  moon  and  the  earth  is  equal  to  the  weight  (at  the  earth's 
surface)  of  twenty  quadrillion  tons.  The  weight  of  the  moon's  mass  at 
the  earth's  surface  would  be  about  3,600  times  as  great  as  this.  The 
forces  exerted  among  astronomical  bodies  are  inconceivably  immense 
only  because  the  masses  of  these  bodies  are  so  vast ;  but,  owing  to  the 
great  distances  between  the  bodies,  the  forces  are  small  as  compared 
with  the  weight  of  equal  masses  at  the  earth's  surface. 

It  was  from  the  mathematical  laws  governing  the  motions  of  the 
planets,  the  forms  and  sizes  of  their  orbits,  and  their  times  of  revolu- 
tion in  these  orbits,  that  Newton  deduced  the  Law  of  Gravitation. 

Weight  is,  as  has  been  stated,  merely  a  familiar  example 
of  universal  gravitation.  As  the  earth  is  nearly  a  sphere, 


WEIGHT  ABOVE  AXD  BELOW  EARTH'S  SURFACE.     121 


weight  acts  toward  its  center.  A  cord,  by  which  any  body 
is  suspended — e.  g.,  a  plumb-line — will  then  be  always  ver- 
tical— that  is,  will  point  toward  the  center  of  the  earth. 

This  statement,  however,  is  not  strictly  true.  A  plumb-line  at  the 
foot  of  a  mountain  will  not  hang  precisely  vertical ;  but  its  lower  end  will 
incline  a  little  toward  the  mountain  because  the  mass  of  the  bob  will 
be  sensibly  attracted  sidewise  by  that  of  the  mountain.  The  amount 
of  this  inclination  is  very  slight,  but  has  been  indirectly  measured. 

Weight  above  and  below  the  Earth's  Surface. — 

Bodies  become  lighter  as  they  are  taken  up  from  the  earth's 
surface ;  but  since  the  force  diminishes  as  the  square  of  the 
distance  from  the  center  (not  from  the  surface)  of  the  earth, 
and  as  the  center  is  4,000  miles  below  the  surface,  the 
diminution  is  small.  F 

A  body  weighing  1,000  pounds  at  the  earth's 
surface  would  weigh  (on  a  spring-balance  gradu- 
ated at  the  surface)  only  one  pound  less  at  a 
height  of  two  miles.  At  the  distance  of  the 
moon  from  the  earth  (240,000  miles),  the  same 
body  would  weigh  less  than  five  ounces.  2  x  4ooo}-j-ib. 


lib. 


A  body  below  the  surface  of  the  earth 
weighs  less  than  at  the  surface  because 
some  of  the  mass  of  the  earth  is  now  at- 
tracting upward.  At  the  center  of  the 
earth  the  body  would  have  no  weight. 

For  example,  a  body  at  P  (Fig.  32)  would 
have  above  it  all  that  portion  of  the  earth  in- 
cluded between  the  plane  A  P'  B  and  the  surface 
A  P  B.     This  portion  would  be  attracting  it  up- 
ward— i.  e.,  toward  the  surface — while  the  rest 
would  be  pulling  it  downward— i.  e.,  toward  the  center.     The  result- 
ing downward  pull  would  be  the  difference  between  these  two.     At 
the  center,  the  portions  on  opposite  sides  of  any  plane  would  be  equal. 

Falling-  Bodies. — All  free  bodies,  whatever  their  mass, 
fall  toward  the  earth  with  equal  accelerations.     If  one  body 

possesses  twice  the  mass  of  another,  twice  the  force  will 
9 


FIG.  32.— DIMINUTION 
IN  WEIGHT  ABOVE 
AND  BELOW  THE 
EARTH'S  SURFACE. 


122  GRAVITATION  AND  THE  PENDULUM. 

be  required  to  give  it  the  same  acceleration ;  but  the  weight 
is  proportional  to  the  mass,  and  the  weight  is  the  force 
causing  the  fall.  Hence  the  body  of  twice  the  mass  has 
twice  the  force  (weight)  acting  upon  it,  and  therefore  moves 
with  the  same  acceleration.  The  size,  shape,  and  material, 
make  no  difference,  for  the  acceleration  of  a  free 
body  is  determined  only  by  its  mass  and  the  acting 
force. 

But  bodies  falling  through  air  are  not  entirely 
free,  for  the  air  offers  a  resistance  tending  to  retard 
their  motion.  This  resistance  is  due  partly  to  fric- 
tion, partly  to  the  work  necessary  to  displace  the 
air  in  front  of  the  moving  body.  Its  amount  is 
greater  the  faster  the  body  moves,  the  larger  the 
body  is  in  proportion  to  the  mass,  and  the  more 
irregular  its  shape. 

Thus  some  objects,  such  as  the  seeds  of  dandelions  and 
thistles,  or  feathers,  wool,  fine  dust,  a  spread  umbrella  point 
upward,  fall  very  slowly  through  air,  while  bodies  of  equal 
mass  in  compact  form  would  fall  much  faster. 

This  may  be  illustrated  by  an  experiment  with  the 
"  guinea  and  feather  tube  "  (Fig.  33),  a  long  glass  tube  con- 
taining a  coin  and  a  feather  or  bit  of  paper.  Invert  the 
tube,  and  you  will  see  the  metal  drop  quickly  to  the  bottom 
while  the  feather  falls  slowly,  just  as  they  would  act  in  the 
.  a*r  outside.  Connect  the  tube  with  the  air-pump  and  ex- 
haust part  of  the  air.  The  metal  will  still  fall  faster  on  in- 
verting the  tube,  but  the  feather  less  slowly  than  before.  Pump  out 
all  the  air  possible.  The  feather  will  now  fall  nearly  or  quite  as  fast 
as  the  metal.  If  you  could  remove  all  the  air,  they  would  fall  equally 
fast,  and  both  would  fall  slightly  faster  than  the  metal  did  through 
the  air. 

Free  Falling  Bodies  move  with  Uniformly  Ac- 
celerated Motion. — This  fact  has  been  established  by 
careful  .measurements,  and  yet  the  statement  is  not  strictly 
true.  Uniform  acceleration  can  be  produced  only  by  a  con- 
stant force,  and  the  weight  of  bodies  increases  slightly  as 


FALLING  BODIES.— PROJECTILES.  123 

they  approach  the  earth.    Weight  is  sensibly  constant,  how- 
ever, within  vertical  distances  of  a  few  thousand  feet. 

Falling  bodies,  therefore,  afford  a  special  example  of  uni- 
formly accelerated  motion,  and  must  follow  the  laws  given 
on  page  20.  The  rate  of  acceleration  at  places  not  far  from 
latitude  45°  and  not  more  than  a  mile  above  sea-level,  is 
about  980  centimetres  or  32-2  (roughly  32)  feet  per  second. 
This  is  the  quantity  a  in  the  formulae,  and  is  often  denoted 
by  g.  0  wing  to  the  resistance  of  the  air,  results  calculated 
by  these  laws  for  bodies  falling  in  air  will  be  inexact.  If  a 
stone  falls  in  air,  it  will  meet  with  a  continually  increasing 
resistance.  After  it  has  fallen  a  few  hundred  feet,  this  re- 
sistance will  become  equal  to  its  weight,  so  that  the  body 
will  cease  to  be  accelerated  and  will  fall  at  a  uniform  speed. 

Projectiles. — A  bullet  discharged  from  a  gun,  an  arrow 
from  a  bow,  a  stone  thrown  by  the  hand,  are  examples  of 
Projectiles.  The  figures  on  pages  55  and  56  show  the  paths 
which  projectiles  would  take  on  being  discharged  at  various 
angles  to  the  horizontal,  provided  no  resistance  were  offered 
by  the  atmosphere.  The  path  A  B'  C'  would  be  in  any  case 
a  portion  of  a  curve  called  a  parab'ola. 

It  may  be  shown  mathematically  that  the  horizontal  distance  A  I', 
which  a  projectile  would  traverse  before  coming  to  the  ground,  if 
started  with  a  given  velocity,  will  be  greatest  when  the  initial  direc- 
tion A  B  is  at  an  angle  of  45°  to  the  horizontal.  If  fired  at  a  greater 
or  less  angle,  the  projectile  would  reach  the  ground  sooner.  The  actual 
best  angle  is  somewhat  less,  owing  to  the  resistance  of  the  air.  In  what- 
ever direction  the  projectile  is  thrown,  the  air  continuously  retards  its 
motion.  Thus,  if  it.  were  not  for  air  resistance,  a  body  thrown  upward 
would  have  the  same  velocity  on  reaching  the  earth  as  at  starting ; 
but  the  air  continuously  slows  its  speed,  so  that  it  rises  less  high  and 
strikes  the  ground  with  less  velocity  than  it  otherwise  would. 

QUESTIONS.  — Wliat  is  Universal  Gravitation  ?  To  what  form  of  energy  is  it  due  ? 
State  the  law  of  gravitation.  In  reckoning  the  attraction  of  a  sphere,  at  what 
point  may  we  consider  its  mass  as  concentrated  ?  How  much  time  does  it  re- 
quire for  gravitation  to  act  between  sun  and  earth  ?  Is  gravitation  affected  by 
interposing  objects  between  the  attracting  particles  ? 


124  GRAVITATION  AND  THE  PENDULUM. 

What  is  meant  by  the  term  Weight  ?  In  what  direction  does  weight  act  ?  At  what 
rate  does  weight  diminish  as  we  ascend  from  the  earth's  surface  ?  A  man  who 
learned  that  weight  diminishes  as  the  square  of  the  distance,  proposed  that 
soldiers  should  carry  their  knapsacks  supported  on  the  muzzles  of  their  mus- 
kets, as  the  knapsacks  would  then  be  about  twice  as  far  from  the  ground  and 
would  therefore  weigh  but  one  fourth  as  much.  Where  was  his  fallacy  ?  Why 
does  weight  diminish  as  we  descend  into  the  earth  ?  What  do  we  mean  by  "  up  " 
with  reference  to  gravity  ? 

At  the  bottom  of  a  mine  1,000  feet  deep,  how  much  would  the  mass  of  a  pound 
weigh  ?  How  much  at  a  height  of  1,000  feet  above  the  surface  ?  Does  weight 
diminish  more  rapidly  in  descending  into  the  earth  or  in  rising  above  it  ?  What 
would  be  the  weight  of  a  body  at  the  center  of  the  earth  ?  What  would  be  its 
mass  ?  Does  weight  have  anything  to  do  with  producing  the  mass  of  a  body  ? 
Does  mass  have  anything  to  do  with  producing  the  weight  of  a  body  ? 

With  what  kind  of  motion  do  free  bodies  fall  toward  the  earth  ?  What  kind  of 
force  is  necessary  to  produce  uniformly  accelerated  motion  ?  Is  it  then  strictly 
true  that  the  motion  of  freely-falling  bodies  is  uniformly  accelerated  ?  Why 
does  it  appear  true  in  our  ordinary  experiments  ?  If  a  body  were  to  fall  to- 
ward the  earth  (in  a  vacuum),  would  its  rate  of  acceleration  slightly  increase  or 
slightly  diminish  ?  Why  ?  If  a  body  were  falling  down  the  shaft  of  a  mine  (in 
a  vacuum),  what  would  be  the  change  in  its  rate  of  acceleration  ? 

What  is  the  effect  of  air  upon  the  motion  of  falling  bodies  ?  What  is  meant  by  a 
projectile  ?  Why  do  projectiles  near  the  earth's  surface  not  travel  in  straight 
lines  ?  If  a  projectile  were  moving  in  free  space  at  such  a  distance  from  all 
bodies  that  gravitation  was  insensible,  in  what  path  would  it  move  ?  Why  ? 

In  the  following  problems,  the  resistance  of  the  air  is  to  be  disregarded  unless 
otherwise  stated  :  In  a  freely-falling  body  what  would  be  the  velocity  after 
3  seconds  ?  How  long  would  it  take  a  body  to  acquire  a  velocity  of  3,220  feet  a 
second  ?  How  far  will  a  body  fall  in  one  second  ?  In  two  seconds  ?  In  three  ? 
In  four  ?  How  far  does  it  fall  during  the  first  second  ?  During  the  next  ?  Dur- 
ing the  third  ?  The  fourth  ?  How  long  will  it  take  a  body  to  fall  100  feet  ?  A 
stone  is  dropped  or  thrown  horizontally  from  the  top  of  a  cliff  and  reaches  the 
bottom  in  3'5  seconds.  How  high  is  the  cliff  ?  A  stone  is  thrown  vertically 
upward  with  a  velocity  of  50  feet  a  second.  How  high  will  it  rise  ?  How  long 
will  it  remain  in  the  air  ? 

Does  the  resistance  of  the  air  arrest  or  oppose  gravity  in  the  case  of  projectiles  ? 
Can  you  think  of  a  reason  why  wind-gauges  are  used  on  rifles  ?  If  a  '44-inch 
caliber  bullet  were  discharged  vertically  upward  from  a  Winchester  rifle, 
would  it  gather  sufficient  energy  in  its  descent  to  strike  with  fatal  effect  ? 
Would  a  charge  of  swan-shot  ?  Why  ?  Can  you  conceive  how  the  laws  relat- 
ing to  projectiles  are  taken  advantage  of  in  military  science  ? 


CENTER  OF  MASS. 

Center  of  Weight  or  Mass. — Let  A  and  B  be  two 

homogeneous  spherical  particles  of  any  size  and  mass.  Sup- 
pose them  to  be  connected  by  a  rigid  rod,  which  for  con- 
venience we  will  assume  to  have  no  mass.  Let  the  lines 


CENTER  OF  MASS. 


125 


FIG.  34.— RESULTANT  OP  WEIGHT  OF  SYSTEM 
PASSES  THROUGH  CENTER  OF  MASS. 


Wl  and  W2  represent  their  weights.  These  will  be  propor- 
tional to  their  masses,  and  will  act  as  if  the  mass  of  each  were 
concentrated  at  its 
center.  Then  Wl  and 
W2  form  a  pair  of 
parallel  forces  in  the 
same  direction.  Their 
resultant  will  be  par- 
allel to  them  and 
equal  to  their  sum — 
i.  e.,  R  =  Wj  +  W2. 
The  distance  of  the 
resultant  from  each 

will  be  such  that  Wj  X  a  c  =  W2  X  b  c — that  is,  so  that 
a  c  :  b  c  =  W2  :  W^  For  example,  if  Wl  =1,  and  W8  =  3, 
then  #  c  :  #  e  =  3  :  1,  OT  a  c  must  be  three  times  b  c. 

If  a  b  is  not  horizontal,  then  let  Fig.  35  represent  any 
other  position.  Now,  R  must  always  be  parallel  to  Wt  and 
W2,  and  at  such  a  distance  that  Wl  X  a  c  =  W2  X  b  c — that  is, 

that  a  c  :  b  c  =  W,  :  Wt. 
For  W2  :  W,  =  af :  ef, 
and  a  c  :  b  c  =  af :  ef. 
Hence  a  c  :  b  c  =  W2 :  Wj. 
This  is  true  for  any  angle 
fw2  or  position  whatever  of 
the  rod.  Hence  the  re- 
sultant always  passes 
through  one  common 
point,  c,  whatever  the 
position  of  the  system. 
If,  therefore,  a  force 
equal  and  opposite  to  R  were  applied  at  c,  it  would  counter- 
balance the  weight  of  A  and  B  and  hold  up  the  system  just 
as  if  all  the  mass,  and  therefore  all  the  weight,  were  concen- 
trated at  c.  The  point  c  is  called  the  Center  of  Mass,  being 
the  middle  point  of  the  mass  of  the  body.  It  is  also  known 


FIG.  35.— RESULTANT  PASSES  THROUGH  CENTER 
OF  MASS  IN  ANY  POSITION  OF  SYSTEM. 


126 


GRAVITATION  AND  THE  PENDULUM. 


as  the  Center  of  Weight,  or  (as  weight  is  merely  a  special 
case  of  gravitation)  the  Center  of  Gravity  of  the  system. 

If  instead  of  two  particles  there  were  three,  we  should  proceed  in 
a  similar  manner  to  find  the  resultant  of  the  three  weights  in  one  posi- 
tion of  the  system,  then  in  another,  and  so  on ;  and  the  intersection  of 
all  these  resultants  would  be  the  center  of  mass  of  the  system.  Bodies 
are  merely  collections  of  particles.  Hence 

The  Center  of  Mass  (of  Gravity,  or  of  Weight]  of  a  body 
is  the  common  point  through  which  the  resultant  of  the  weight 
of  all  its  parts  passes,  whatever  the  position  of  the  body. 

On  consideration,  you  will  see  that  the  center  of  mass  of  a  body  is 
in  general  not  at  what  we  should  call  the  middle  of 
the  body— that  is,  at  the  center  of  its  volume— un- 
less the  body  is  homogeneous.  A  circle  of  wood,  if 
homogeneous,  would  have  its  center  of  mass  at  its 
geometrical  center ;  but  if  a  plug  of  lead  were  put 
into  it  at  a  (see  Fig.  36),  the  center  of  mass  would 
be  at  some  position  c',  between  c  and  a. 


EQUILIBRIUM  OF  BODIES  IN  RESPECT  TO  WEIGHT. 

A  Body  is  said  to  be  in  Equilibrium  with  respect 
to  its  weight  when,  on  being  left  to  itself,  motion  does  not 
ensue.  Let  A  (Fig.  37)  be  any  body  supported  on  a  pivot 

or  axis  at  «,  about  which  it  is 
free  to  turn.  The  body  will 
always  come  to  rest  with  its 
center  of  gravity  c  vertically  un- 
der #,  as  shown  in  the  figure  :  for, 
suppose  it  pulled  to  one  side,  so 
that  c  is  at  c' ;  then  the  weight 
"W  will  have  a  moment  Wx«'  V, 
tending  to  turn  A  around  a'  as  a 
pivot.  The  only  position  in 
which  the  moment  is  zero  is 
where  a'  V  is  zero — i.  e.,  when  c  is  vertically  above  or  below  a. 


FIG.  37.— EQUILIBRIUM  WHEN  CEN- 
TER OP  MASS  IS  VERTICALLY 
ABOVE  OR  BELOW  POINT  OF 
SUPPORT. 


EQUILIBRIUM  OF  SUSPENDED  BODIES. 


127 


The  body  then  can  remain  at  rest  when  left  to  itself — that 
is,  can  be  in  equilibrium  (in  respect  to  weight)  only  when 
the  center  of  mass  is  vertically  above  or  below  the  point  of 
support.  This  is  true  of  all  pivoted  bodies. 

Plumb-line. — Suppose  the  body  A  is  suspended  from  a 

point  a  by  a  flexible  cord 
d  a.  When  the  body  is  at 
rest,  its  center  of  mass,  c, 
and  the  points  a  and  d, 
will  all  be  in  the  same  ver- 
tical line,  and  the  cord  d  a 
will  therefore  be  vertical; 
for,  if,  either  a  or  c  is  out 
of  the  vertical,  there  will  be 
a  moment  due  to  the  weight 
and  tending  to  bring  them 
back  into  the  vertical,  as  in 
Fig.  37. 

If  the  suspended  body  P 
(Fig.  38)  be  homogeneous  and 
carefully  turned  to  a  point,  and 
the  cord  be  put  in  at  the  proper 

place,  the  point  of  P  will  also  be  vertically  below  the  supporting  point. 
Such  an  arrangement  is  used  by  surveyors  and  others  for  obtaining 
vertical  lines,  and  is  called  a  plummet  or  plumb-line,  because  the 
body  P  is  sometimes  made  of  lead  (Latin,  plumbum)  on  account  of 
the  great  density  of  that  metal.  The 
line  itself  is  necessarily  vertical,  what- 
ever the  bob  be  made  of,  and  what- 
ever its  shape. 

Why  does  the  knife  suspended  at 
A  (Fig.  39)  hang  in  the  position  rep- 
resented when  in  equilibrium  ? 

To    find    the    Center   of 

Mass.— The  principle  that  the 

center  of  mass  of  a  free  body,  when  in  equilibrium,  is  verti- 
cally under  or  over  the  point  of  support,  is  made  use  of  to 


FIG.  38.— PLUMMET  FOB  OBTAINING  VER 
TICAL  LINES. 


128 


GRAVITATION  AND  THE  PENDULUM. 


find  experimentally  the  position  of  this  center.  Let  the 
body  be  hung  successively,  from  several  different  parts. 
Notice  the  direction  of  the  suspending  cords  relatively  to 
the  body.  These  directions  will  all  intersect  at  one  point, 
which  will  be  the  desired  center  of  mass. 

By  way  of  experiment,  take  a  piece  of  cardboard  of  any  shape,  say 
A  B  C  D.  Hang  it  by  a  cord  h  a  through  a  and  note  the  direction 

h  a  d  of.  the  cord  (prolonged). 
Or,  better,  put  a  long  pin  through 
a  hole  at  a.  Hang  over  the  pin 
a  little  plumb-line,  made  of  a 
thread  and  a  bit  of  any  heavy 
substance.  Mark  with  a  pencil 
two  points  on  the  cardboard  just 
behind  the  plumb-line,  and  draw 
a  straight  line  through  them.  Do 
the  same  for  one  or  more  other 
holes,  b,  e,  etc.  These  lines 
(dotted)  will  intersect  at  or  near 
the  same  point,  c,  which  is  the 
desired  center  of  mass — for  the 
center  of  mass  must  lie  in  each 
line,  and  therefore  at  the  inter- 
section. Balance  a  fork,  cane,  or 

chair,  on  the  finger  or  hand.     The  center  of  mass  will  be  at  the  intersec- 
tion of  verticals  through  the  hand  for  different  positions  of  the  object. 

Stable  and  Unstable  Equilibrium. — If,  in  Figs.  37 
to  40,  c  be  vertically  below  #,  then,  on  pulling  c  to  one  side, 
the  weight  will  tend  to  drag  the  body  back  to  its  position 
of  rest.  This  condition  is  called  one  of  stable  equilibrium. 
In  general,  equilibrium  is  said  to  be  stable  when,  on  being 
moved,  the  body  tends  to  return  to  its  original  position. 

If  c  be  vertically  above  #,  then,  on  the  slightest  motion, 
the  weight  tends  to  tip  the  body  still  farther.  This  condi- 
tion is  called  one  of  unstable  equilibrium.  In  general,  equi- 
librium is  unstable  when,  on  being  moved,  the  body  tends 
to  depart  still  farther  from  its  original  position.  In  the  case 
of  a  suspended  body  it  is  difficult,  if  not  impossible  (unless 


FIG.  40.— ILLUSTRATING  METHOD  OF  FIND- 
ING CENTER  OF  MASS.      • 


EQUILIBRIUM   OF  BODIES  ON  SURFACE.  129 


there  is  considerable  friction),  to  adjust  the  body  in  the 
position  of  unstable  equilibrium. 

Neutral  or  Indifferent  Equilibrium. — If  the  point 
of  suspension  a  coincides  with  the  center  of  mass  c,  then  the 
body  will  remain  in  any  position  in  which  it  is  placed,  be- 
cause the  weight  always  acts  directly  through  the  supporting 
point,  and  its  moment  must  always  be  zero.  This  condition 
is  called  neutral  or  indifferent  equilibrium.  It  is  the  con- 
dition in  which  the  body,  on  being  moved,  tends  neither  to 
return  to,  nor  to  move  farther  from,  its  original  position. 

Equilibrium  of  Bodies  resting  on  a  Surface. — If 

any  body,  A,  is  resting  on  a  surface  at  only  one  point,  #,  and 
c  be  its  center  of  mass,  as  in  Fig.  41, 
then  it  is  evident  that  A  is  not  in  equi- 
librium, and  can  only  be  so  when  c  is 
directly   over  a.     Its   equilibrium   will 
then  also  be  unstable.     If  the  body  is  a 
spherical  one,  or  a  circular  one  stand- 
ing on   edge   on   a  horizontal    surface 
(Fig.  42),  c  will   necessarily  be   always 
vertically  over  «,  and  the  body  will  be 
always  in  neutral  equilibrium.    A  sphere 
or   vertical   circle   on  an  inclined  surface  can  never  be  in 
equilibrium,  because  c  can  not  be  over  a.     Any  body  what- 
ever (Fig.  4:2)  on  an  inclined  surface  will  be  in  equilibrium 

whenever  its  center 
of  gravity  c  is  over 
its  point  of  support 
a,  and  only  then. 
The  fact  that  the 
surface  is  inclined, 
so  that  perhaps  the 
body  may  slide 
down,  has  nothing 


vw 

FIG.  41.— STONE  TOUCH- 
ING AT  ONE  POINT. 


FIG.  42.— EQUILIBRIUM  IN  CASE  OF  BODIES  RESTING 
ON  SURFACE. 


to  do  with  the  equilibrium  of  the  body  itself. 


130  GRAVITATION   AND  THE  PENDULUM. 

The  Base. — Bodies  standing  by  themselves  are  ordi- 
narily supported  by  three  or  more  points.  A  three-legged 
stool  rests  upon  the  floor  at  the  points  a,  #,  and  e,  Draw 
lines  a  #,  b  e,  e  a.  The  surface  a  b  e  inclosed  by  these  lines 
is  called  the  Base.  If  the  body  rests  at  several  points,  the 
base  is  the  surface  inclosed  by  the  lines  circumscribing  those 
points.  For  instance,  if  a  body  rests .  on  the  points  abed 

c 
a-^  .,        -4    X 


a 

FIG.  43.— ILLUSTRATING  THE  BASK.  FIG.  44. 

e  f  g  h  I  (Fig.  44),  the  base  would  be  the  surface  inclosed  by 
a  cfg  I 

A  body  is  in  stable  equilibrium  only  when  the  vertical 
through  the  center  of  mass  passes  through  the  base.  As  soon 
as  the  vertical  falls  outside  the  base,  the  equilibrium  ceases 
and  the  body  overturns. 

The  Degree  of  Stability  depends  on  the  work  neces- 
sary to  overturn  the  body — that  is,  to  destroy  its  stability. 
Let  A  and  B,  Fig.  45,  represent  the  same  body  lying  on  its 
side  and  standing  on  end.  Its  degree  of  stability  is  greater 
in  the  former  than  in  the  latter  position.  Why?  Because 
to  overturn  it,  more  work  must  be  done. 

What  is  the  work  to  be  done  I  Take  the  first  position  A.  To 
destroy  the  equilibrium,  we  must  bring  c  up  to  such  a  point  c'  that  the 
vertical  c'  d  falls  just  beyond  b.  This  requires  that  the  whole  mass  of 
the  body  be  raised.  We  must  do  work,  therefore,  against  the  weight 
of  the  body,  and,  as  the  weight  may  be  considered  as  acting  through 
the  center  of  mass,  the  amount  of  work  done  will  be  the  product  of  the 
weight  into  the  vertical  distance  d  c',  through  which  the  body  has  been 
raised.  In  the  position  represented  in  B,  the  weight  is  the  same,  but 


DEGREES  OF  STABILITY. 


131 


the  height  d'  c'  is  much  less.     The  work  to  be  done  is  proportionately 
less.    Hence  the  stability  is  much  greater  on  the  broader  base. 


b'  a  b 

FIG.  45.— ILLUSTRATING  DEGREES  OP  STABILITY. 

If  the  body  C  is  of  the  same  weight  as  A,  and  has  the  same  size 
and  shape  of  base,  but  is  of  such  a  shape  or  density  that  its  center  of 
mass  is  much  higher,  then  it  will  be  less  stable — for  the  height  d"  c' 
will  be  less,  and  the  work  done  correspondingly  less. 

Of  two  bodies  with  the  same  base  and  center  of  mass  at  the  same 
height,  but  of  different  weights,  the  heavier  will  be  the  more  stable, 
because  the  work  required  to  overturn  it,  being  the  product  of  the 
weight  into  d  c',  will  be  greater.  To  determine,  then,  which  of  several 
bodies  or  of  several  different  positions  of  the  same  body  is  the  most 
stable,  we  must  ascertain  which  requires  the  greatest  work  to  be  done 
in  order  to  destroy  the  equilibrium  by  overturning  the  body. 

If  it  is  desired  to  have  any  Object  or  Structure 
stable,  it  is  necessary  to  see  that  the  center  of  gravity  shall 
be  over  the  base.  To  secure  the  greatest  degree  of  stability 
possible,  care  must  be  taken  to  arrange  matters  so  that  the 
amount  of  work  required  to  overturn  the  object  shall  be  as 
great  as  possible.  This  is  usually  accomplished  by  making 
the  base  large  and  the  center  of  mass  low. 

QUESTIONS.— Define  center  of  mass  ;  center  of  weight ;  center  of  gravity.  Why 
are  the  center  of  mass  and  the  center  of  weight  at  the  same  point  ?  Suppose 
two  particles,  of  mass  5  and  1  respectively,  to  be  connected  by  a  rigid  rod  of 
length  10  and  without  weight — show  where  their  center  of  mass  is  located.  Are 
the  center  of  mass  and  the  geometrical  center  of  bodies  generally  the  same  ? 
Why  ?  When  is  a  body  said  to  be  in  equilibrium  with  respect  to  its  weight  ?  If 
a  body  is  suspended  so  that  it  can  turn  about  a  point,  what  is  the  condition  for 
equilibrium  ?  If  a  body  is  suspended  by  a  flexible  cord,  what  will  be  the  direc- 
tion of  the  cord  when  there  is  equilibrium  ?  Why  ? 

What  is  a  plummet  or  plumb-line  ?  For  what  is  it  used  ?  How  can  you  find 
the  center  of  mass  of  any  body  by  experiment  ?  Explain  the  reason  for  the 


132  GRAVITATION  AND  THE  PENDULUM. 

method.  Suppose  that  you  wished  to  find  the  center  of  gravity  of  a  bat,  how 
could  you  do  so  by  laying  it  across  the  edge  of  a  board  ?  What  are  the  three 
kinds  of  equilibrium  ?  Describe  each.  Give  examples  of  each.  If  a  body  rests 
upon  several  points,  what  constitutes  its  base  ?  What  is  the  condition  of  stable 
equilibrium  for  such  a  body  ?  Why  does  a  man  lean  forward  when  carrying  a 
heavy  load  upon  his  back  ?  If  you  have  a  heavy  weight  in  one  hand,  what 
position  do  you  take  ?  Why  ?  Why  does  a  load  of  hay  tip  over  so  easily  if  on 
a  side-hill  ?  A^coach  with  heavy  baggage  piled  on  top,  on  a  rough  road  ?  What 
do  we  mean  by  saying  that  a  thing  is  top-heavy  ?  Why  does  a  ball  placed  on  a 
sloping  surface  begin  to  roll,  while  a  cube  maintains  its  position  ?  Suppose  that 
a  tall  tower  leans  to  one  side,  how  much  may  it  lean  before  it  will  fall  over  of 
its  own  weight  ?  (Read  about  the  famous  leaning  tower  of  Pisa,  and  of  Galileo's 
experiments  there  with  falling  bodies.) 

Upon  what  does  the  degree  of  stability  of  a  body  depend  ?  Why  does  a  man 
place  his  feet  well  apart  when  he  wishes  to  plant  himself  very  firmly  ?  Where 
is  the  center  of  gravity  in  the  body  of  a  man  ?  Why  does  he  turn  his  toes  out  ? 
Why  use  a  staff  when  he  is  old  ?  Why  can  not  a  person  with  his  heels  against 
the  wall  stoop  without  falling  ? 

Two  blocks  of  wood  of  equal  weight  have  their  centers  of  mass  at  equal  height ; 
one  is  shaped  like  a  pyramid  and  stands  on  its  base,  the  other  is  a  cube  ;  which 
is  the  more  stable  ?  Why  ?  A  certain  wagon  is  loaded  at  one  time  with  a  ton 
of  iron,  at  another  time  with  a  ton  of  hay  ;  in  which  condition  is  it  the  more 
stable  ?  What  are  common  ways  of  making  bodies  stable  ? 

Press  the  head  of  a  needle  firmly  into  the  end  of  a  cork,  and  stick  into  opposite 
sides  of  the  cork  two  forks  sloping  downward  at  equal  angles.  The  whole  may 
now  be  balanced  upon  the  needle's  point.  Why  ? 


THE  PENDULUM. 

The  Simple  Pendulum. — Suspend  a  stone,  or  any 
heavy  object,  A,  from  a  firm  support,  Fig.  46.  Pull  it  an 
inch  or  two  to  one  side  and  let  it  go.  It  will  swing  to  and 
fro  for  a  long  time.  Any  object  oscillating  thus  upon  a 
pivot  or  axis  of  suspension,  by  its  weight,  is  properly  called  a 
Pendulum ;  but  the  term  is  generally  used  to  refer  to  small, 
heavy  objects  hung  by  a  light  suspending  cord  or  wire. 

As  the  pendulum  descends  from  either  extreme  of  its  swing,  it 
gains  velocity  and  therefore  energy,  which  it  loses  again  on  its  upward 
swing  (page  36),  and  which  is  greatest  at  the  lowest  or  middle  point. 
If  energy  can  neither  be  created  nor  destroyed,  whence  comes  this 
energy,  and  where  does  it  go,  the  effects  of  resistance  being  neglected  ? 
Its  source  is  the  energy  of  gravitation  ;  and  in  losing  energy,  the  pend- 
ulum merely  restores  energy  to  that  source.  The  process,  then,  is  a 
periodic  receiving  and  giving  back  of  energy  between  the  stock  of 
gravitational  energy  and  the  pendulum.  To  express  the  idea  in  an- 


LAWS  OF  THE  PENDULUM.  133 

other  way,  the  pendulum  has  at  the  extreme  of  its  path  a  certain  po- 
tential energy  due  to  its  weight  and  its  position,  and  this  potential 
energy  is  converted  gradually  into  actual  (or  kinetic)  energy  in  the  de- 
scent, and  reconverted  into  potential  energy  in  the  ascent.  Consider 
carefully  what  is  meant  by  potential  energy,  and  you  will  see  that  the 
two  forms  of  statement  are  equivalent. 

The  simplest  possible  pendulum  would  be  a  material 
particle  hung  by  a  cord  without  weight.  The  nearest  prac- 
ticable approach  to  this  is  a  small,  heavy  sphere  hung  by  a 
very  light  cord  or  wire.  A  lead  or  brass  ball  suspended  by  a 
braided  silk  cord  works  best,  but  small  stones  hung  on  twine 
will  answer  the  purpose. 

By  the  length  of  a  pendulum  is  meant  the  distance  from 
the  point  of  suspension  to  the  center  of  oscillation.  For  the 
simple  pendulum,  the  center  of  mass  may  be  taken  as  the 
center  of  oscillation. 

The  Laws  of  the  Pendulum  are  as  follows :  The  time 
of  vibration 

I.  Is  independent  of  mass  or  material  of  pendulum. 
II.  Is  independent  of  amplitude,  if  small. 

III.  Is  proportional  to  square  root  of  length. 

IV.  Is  inversely  as  square  root  of  g. 

These  laws  will  be  partly  illustrated  by  experiment. 

EXPERIMENTS  WITH  THE  PENDULUM. — Hang  up  a  stone  or  a  metal 
sphere  B  by  a  cord,  so  that  the  length  of  the  pendulum  (from  b  tc  cen- 
ter of  mass  of  B)  is  the  same  as  that  of  A,  as  nearly  as  you  can  judge. 
Hold  B  aside  as  at  k,  and  at  the  beginning  of  a  minute  by  a  watch  or 
clock  let  it  go.  Count  one  when  it  reaches  Z,  two  when  it  gets  back  to 
k,  three  at  I  again,  and  so  on.  Just  as  one  hundred  is  counted,  note  the 
number  of  seconds  that  have  elapsed.  This,  divided  by  100,  will  give 
the  "  time  of  a  single  vibration,"  or  swing  of  B. 

Pull  A  and  B  aside  and  let  them  go  at  the  same  instant.  You  will 
find  that  they  will  keep  pace  with  each  other  almost  perfectly.  They 
have,  therefore,  the  same  rate  or  time  of  swing. 

Make  another  pendulum  C  out  of  a  wooden  block,  hollow  tennis- 
ball,  or  any  other  substance,  adjusting  its  length  as  nearly  as  possible 
to  equal  that  of  B.  Start  A,  B,  and  C,  swinging  at  the  same  instant. 


134 


GRAVITATION  AND  THE  PENDULUM. 


They  will  keep  pace  very  closely,  the  slight  difference  you  may  observe 
being  due  to  the  fact  that  the  lengths  are  not  exactly  equal.  These 
two  experiments  show  that  the  time  of  vibration  of  pendulums  of  the 
same  length  does  not  depend  on  the  material  of  the  bob. 

Adjust  the  length  of  B  carefully,  until  by  trial  it  keeps  exact  pace 
with  A  when  they  are  started  by  drawing  aside  just  one  inch.    Then 

draw  A  aside  one  inch,  and 
B  two  inches,  and  let  them 
go.  They  will  still  keep 
pace.  Draw  A  aside  one 
inch  and  B  three  inches. 
They  will  still  keep  pace. 
This  shows  that  the  time  of 
vibration  is  independent  of 
the  distance  swung  through, 
which  is  called  the  Ampli- 
tude of  the  Vibration.  The 
law  holds  so  long  as  the 
amplitude  is  not  very  great, 
but  is  not  strictly  true  for 
wide  swings.  This  prop- 
erty is  called  the  Isoch'ron- 
ism  of  the  Pendulum,  and 
is  an  essential  fact  in  the 
application  of  the  pendu- 
lum to  the  exact  measure- 
ment of  time.  It  was  first  noticed  by  Galileo,  who  observed  that  the 
great  chandelier  in  the  cathedral  of  Pisa  swung  in  equal  times  without 
regard  to  the  amplitudes  of  the  swing. 

Hang  a  fourth  pendulum,  D,  of  a  length  equal  to  one  fourth  that 
of  B.  Set  B  and  D  swinging  at  the  same  instant.  You  will  see  that 
D  makes  two  swings  to  one  of  B.  The  time  of  one  swing  of  B,  then, 
is  twice  that  of  D.  The  length  of  B  is  four  times  that  of  D.  There- 
fore, the  time  of  B  :  time  of  D  =  2  :  1.  But  2:1  =  square  root  4  : 
square  of  1.  Hence  the  times  of  vibration  of  pendulums  of  different 
lengths  are  proportional  to  the  square  roots  of  their  lengths. 

Vary  the  length  of  B  until  its  time  of  swing  is  just  one  second. 
Measure  as  carefully  as  you  can  the  distance  from  the  point  of  sup- 
port to  the  center  of  mass  of  B.  It  will  be  a  little  less  than  a  metre 
— i.  e.,  about  39  inches.  At  latitude  45°,  sea-level,  the  length  of  the 
seconds  pendulum  is  '99356  metre  =  39-117  inches. 

The  length  I  of  a  simple  pendulum  to  swing  in  a  time  t,  or 


FIG.  46.— FORMS  OF  THE  PENDULUM.— VIBRA- 
TION  ILLUSTRATED. 


CLOCK  PENDULUM. 


135 


B 


the  time  of  swing  for  a  length  I,  can,  therefore,  be  found  from  the 
formulae : 

7  =  39-117  x  t2  and  t  =  the  square  root  of  ^r-  ,  for  I  in  inches. 

0*7*1 

I  =  -99356  x  <2  and  t  =  the  square  root  of  ^ ,  for  I  in  metres. 

The  time  of  vibration  would  be  less  at  a  place  where  the  force  of 
gravity  is  greater,  because  the  accelerating  force  (weight)  would  be 
greater  for  the  same  mass  in  the  pendulum,  which  would,  therefore, 
move  faster.  The  pendulum  thus  affords  the  most  accurate  means  of 
determining  the  value  of  g  in  different  places. 

Application  of  the  Pendulum  to  Clocks. — The  iso- 
chronism  of  the  pendulum  is  utililized  in  the  measurement  of 
time — in  subdividing  the  astronomical  unit  of  time,  the  day, 
into  hours,  minutes,  and  seconds.  Fig. 
47  shows  the  essential  parts  of  the  mech- 
anism for  this  application,  and  when 
the  following  description  is  studied, 
some  pendulum-clock  should  be  exam- 
ined by  the  pupil.  The  function  of  the 
pendulum  is  solely  to  regulate  the  rate 
of  motion  of  the  works,  so  that  the 
wheels  (which  carry  the  hands  indicat- 
ing the  time)  shall  turn  at  exactly  the 
proper  and  constant  rate. 

The  source  of  energy  maintaining 
the  motion  of  a  clock  is  usually  elastici- 
ty acting  by  a  coiled  spring,  or  gravity 
acting  through  "  weights "  hung  on 
a  cord  wound  over  an  axle.  The  work 
which  this  energy  has  to  perform  is  to 
move  the  clock-works  against  their  fric- 
tion, and  to  keep  up  the  motion  of  the 
pendulum,  which  would  otherwise  grad-  FlG  47<_EsCAPEMENT  OF 
ually  come  to  rest.  Why  ?  CLOCK. 

A  train  of  wheel-work  similar  to  that  of  Fig.  58  (page  152)  trans- 
mits the  pressure  and  motion  to  a  toothed  wheel  called  the  scape- 


136 


GRAVITATION  AND  THE   PENDULUM. 


wheel,  shown  at  D  E  and  D'  E'  (Figs.  47  and  48),  and  pivoted  at  F. 
Let  us  suppose  that  this  wheel  tends  thus  to  rotate  right-handedlyc 
A  C  B  is  a  curved  piece  of  metal  called  the  pallet,  having  at  each  end, 
A  and  B,  a  tooth  or  projecting  point.  It  is  fastened  at  C'  to  the 
spindle  A'  H',  which  is  pivoted  at  both  ends, 
and  to  this  is  also  attached  the  bent  rod  or 
wire  H'  G'  G,  called  the  crutch.  This  whole 
mechanism  is  the  escapement.  The  pendulum 
P  hangs  from  a  fixed  point  I',  its  upper  part 
being  composed  of  a  thin  flexible  metal  strip, 
I'  J',  and  it  passes  through  the  crutch  at  G  G'. 
Let  us  follow  the  action,  starting  with  the 
position  shown  in  Fig.  47.  A  tooth  of  the 
scape-wheel  is  pressing  against  the  pallet-tooth 
at  B,  owing  to  the  pressure  of  the  spring  or 
weights,  and  the  wheel  is  thus  held  from  mov- 
ing. The  pallet-tooth  A  is  free  of  the  wheel; 
The  crutch  and  pendulum  are  at  one  extreme 
of  the  swing,  and  will  therefore  now  begin  to 
swing  back.  When  the  pendulum  becomes 
about  vertical,  the  pallet  will  have  turned  so 
that  its  end  A  will  have  descended  into  the 
space  between  two  teeth  at  E,  and  the  end  B 
will  have  risen  just  enough  to  release  the  scape- 
wheel  tooth.  The  scape-wheel  will,  therefore, 
jump  forward  until  the  following  tooth  strikes 
the  pallet  at  A,  advancing  thus  by  about  the 
space  of  half  a  tooth.  The  pendulum,  con- 
tinuing its  swing,  will  reach  its  right-hand  ex- 
treme, and  will  then  turn  and  swing  back,  the 
pallet  at  A  presently  releasing  the  scape- 
wheel,  which  then  advances  another  half-tooth 
until  stopped  by  the  pallet  at  B.  This  process 
goes  on  continuously,  the  scape-wheel  advancing  a  whole  tooth  for 
each  double-swing  of  the  pendulum. 

The  energy  necessary  to  overcome  air  resistance,  etc., 
and  thus  to  maintain  the  pendulum  in  motion  when  once 
started,  is  supplied  to  it  from  the  scape-wheel  through  the 
pallet  and  crutch.  Start  again  with  the  first  position  of 
Fig.  48.  The  wheel  is  then  pushing  up  the  pallet  at  B', 


FIG.  48.— PALLET  AND 
CRUTCH. 


BALANCE-WHEEL.  137 

owing  to  its  pressure  on  the  sloping  pallet  surface,  and  this, 
of  course,  pushes  the  crutch,  and  the  crutch  in  turn  the 
pendulum,  to  the  right,  adding  to  their  energy.  Such  ac- 
tion continues  until  the  pallet  releases  at  B'  and  engages  at 
A'.  From  the  right-hand  end  of  the  swing  downward,  the 
wheel  similarly  pushes  upward  the  end  A'  of  the  pallet. 

The  Balance-Wheel  replaces  the  pendulum  in  watches 
and  some  clocks.  It  consists  of  a  pivoted  wheel  which 
swings  to  and  fro  on  its  axis  in  equal  times,  owing  to  the 
elasticity  of  a  spring  attached  to  it. 

QUESTIONS.  —What  is  a  pendulum  ?  What  is  meant  by  a  simple  pendulum  ?  What 
maintains  the  motion  of  the  pendulum  ?  What  causes  it  to  come  gradually  to 
rest  ?  What  is  meant  by  the  length  of  a  pendulum  ?  State  the  laws  of  the 
pendulum.  Show  how  to  demonstrate  these  laws  by  experiment.  What  is 
meant  by  the  isochronisni  of  the  pendulum  ?  What  is  the  length  of  a  pendulum 
beating  seconds  ?  Beating  half -seconds  ?  Beating  quarter-seconds  ?  How  may 
the  pendulum  be  used  to  measure  the  variations  in  weight  at  different  parts  of 
the  earth's  surface  ?  Explain  the  application  of  the  pendulum  to  clocks. 


MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

Why  is  it  easier  to  carry  the  same  amount  of  water  in  two  pails,  one  in  each 

hand,  than  in  a  single  pail  ? 

Can  you  explain  the  object  of  feathering  your  oars  while  rowing  ? 
How  is  our  earth  kept  in  its  path  about  the  sun  ? 
In  the  latitude  of  New  York,  a  seconds  pendulum  is  about  39  inches  long.     How 

long  must  one  be  to  vibrate  once  in  seven  seconds  ?    How  long  to  vibrate  four 

times  in  a  second  ? 
At  the  equator,  a  pendulum  39  inches  long  vibrates  once  in  a  second.    How  long 

must  a  pendulum  be  to  vibrate  once  in  half  an  hour  ? 

Would  a  plumb-line  on  a  ship's  deck  under  the  rock  of  Gibraltar  hang  perpen- 
dicularly ?    Why  ?    Could  you  easily  detect  the  variation  ? 
Is  there  a  place  between  the  moon  and  the  earth  where  a  body  would  have  no 

weight,  and  would  not  fall  in  any  direction  ?    Explain. 
Would  you  weigh  more  or  less  on  the  moon  than  on  the  earth  ?    Why  ?     Could 

you  jump  farther  on  the  moon  ? 
On  what  principle  may  a  load  of  stone  pass  safely  over  a  hill-side  where  a  load  of 

hay  would  be  overturned  ? 
Have  you  ever  noticed  persons  bend  forward  in  rising  from  a  chair  ?    How  do 

they  change  their  center  of  gravity  in  so  doing  ?    Why  do  you  instinctively 

lean  back  when  descending  a  steep  hill  ?    Do  you  really  incline  your  body  out 

of  the  vertical  in  so  doing  ? 

Does  a  trotting  horse  raise  both  feet  on  the  same  side  at  the  same  time  ?     Why  ? 
When  a  man  is  fishing  with  a  heavy  sinker  in  a  strong  current,  his  line  assumes 
10 


138  FRICTION   AND  MACHINES. 

a  slanting  position.    Can  you  construct  a  diagram  illustrating  the  nature  and 

action  of  the  forces  in  operation  ? 
Is  the  velocity  of  every  particle  of  mud  on  a  revolving  carriage- wheel  the  same  ? 

Why  does  the  mud  fly  off  from  the  felly  and  not  from  the  hub  ? 
How  can  you  determine  whether  a  wall  is  exactly  vertical  ? 
Why  is  your  student's  lamp  made  so  heavy  at  the  base  ? 
Two  pendulums  at  Jacksonville,  Fla.,  vibrate  in  40  seconds  and  10  seconds.    How 

many  times  longer  is  one  than  the  other  ? 
Explain  the  principle  on  which  his  fly-rod,  held  horizontally,  greatly  aids  an 

angler  in  maintaining  his  balance  on  a  thin  tree-trunk  or  a  rounded  log. 


FRICTION  AND  MACHINES. 

NATURE  AND  LAWS  OF  FRICTION. 

Friction  opposes  Motion. — Draw  your  hand  across 
any  surface,  push  a  pile  of  books  along  the  table-top  or  a 
chair  across  the  floor — in  short,  cause  any  two  solid  surfaces 
to  rub  together ;  you  will  find  that  to  keep  up  continuous 
motion  you  must  do  work.  This  is  true  even  if  a  uniform 
velocity  is  maintained,  in  which  case  the  object  is  not  stor- 
ing up  or  giving  out  kinetic  energy.  You  are  moving  the 
body  uniformly  against  a  resistance.  This  resistance  is  at 
the  rubbing  surfaces,  and  is  called  Friction. 

What  is  the  nature  of  frictional  resistance,  and  what  be- 
comes of  the  energy  used  up  in  doing  work  against  friction  ? 
The  second  question  has  been  answered  by  showing  (page  40) 
that  the  rubbing  surfaces  become  hot.  The  energy  is  trans- 
formed into  heat.  Of  the  nature  of  the  resistance  caused 
by  friction,  we  may  form  an  idea  in  the  following  way : 

No  surface  is  perfectly  smooth.  Even  polished  surfaces,  when 
viewed  through  a  glass,  appear  scratched  or  uneven.  The  irregular 
lines  abed  (Pig.  49)  may  represent  a  magnified  section  of  the 
smooth,  rubbing  surfaces  of  two  bodies,  A  and  B.  Notice  how  the 
irregularities  of  these  surfaces  interlock.  Thus,  at  a,  &,  and  d,  for 
instance,  when  moving  over  B  in  the  direction  of  the  arrow,  A  would 
experience  a  resistance  owing  to  the  backward  elastic  pressure  of  the 


SLIDING  FRICTION.  139 

points  of  B.    If,  then,  A  is  pulled  along,  it  must  slide  upward  at  these 

various  points  and  pass  over  them.     This  is  accomplished  partly  by  a 

rise  of  the  whole  body  A,  partly  by 

compressing  or  bending  the  projec-  ^  '"-• T'Bf 

tions  at  the  points  of  contact.     As       r~^'~  jgT  "     ilfe^ 

A  moves  along,  a  multitude  of  such       £;; ^O.-ILLUSTRATING  FRICTION  ol 

little  actions  occur,  which  are  like  RUBBING  SURFACES. 

so  many  slight  blows.    In  this  way, 

vibrations  are  set  up  in  the  particles  of  the  rubbing  surfaces,  and  the 

energy  of  these  constitutes  the  heat  produced  by  the  rubbing. 

It  is  thus  not  difficult  to  conceive  how  the  resistance  of 
friction  is  due  to  the  interlocking  of  roughnesses  of  surface. 
If  the  smoothness  of  the  surface  could  be  made  perfect,  two 
clean  rubbing  surfaces  of  the  same  substance  would  not  dif- 
fer from  two  parts  of  the  same  body  separated  merely  by  an 
imaginary  plane.  The  only  interlocking  then  would  be  due 
to  the  vibration  of  the  molecules  across  that  surface,  which 
of  itself  would  be  enough  to  cause  very  great  friction. 

Laws  of  Sliding  Friction. — Let  A  (Fig.  50)  be  a  block 
of  well-planed  wood  2  by  4  by  8  inches,  sliding  on  a  smooth 
horizontal  board  C.  Let  B  be  a  pulley  turning  with  little 
friction,  over  which  runs  a  cord  attached  to  A  at  E  and 
carrying  a  pan  for  weights  below.  A  spiral  spring  fastened 
to  the  table  and  by  a  cord  to  the  pan  checks  the  descent  of 
the  latter  somewhat  gently,  and  thus  prevents  the  spilling 
of  the  weights.  Put  sand  or  shot  into  the  pan  until,  on  tap- 
ping the  block  A  with  the  finger,  it  will  start  and  keep  up 
its  motion,  but  not  be  accelerated.  Note  the  weight  of  pan 
and  contents  together  and  call  it  w\ ;  also  the  weight  of  the 
block,  and  call  it  W^  Then  wl  is  called  the  amount  of 
"  friction  of  motion  "  of  A  upon  C  under  the  pressure  Wj. 

EXPERIMENTS. — The  amount  of  this  friction  depends  on  the  amount 
of  the  pressure  WL  Put  a  weight  upon  A  so  that  the  pressure  is 
doubled — i.  e.,  is  2  Wx.  Increase  the  load  in  the  pan  until  motion  is 
again  just  kept  up.  On  weighing  the  pan  and  contents,  you  will 
now  find  it  very  nearly  2  w^  If  you  make  the  pressure  3  Wlt  the 
pan-load  will  be  found  3  wlt  and  so  on.  Hence,  the  friction  of  motion 


140 


FRICTION. 


is  proportional  to  the  pressure  with  which  the  surfaces  are  held  in 

contact. 

Remove  the  load  from  A  and  the  pan.     Turn  the  block  over  upon 

a  larger  or  smaller  side,  keep- 
ing the  cord  E  B  still  horizon- 
tal. Load  the  pan  until  mo- 
tion is  just  maintained.  The 
load  will  be  found  equal  to  wl 
or  nearly  so.  It  would  be  ex- 
actly equal  if  the  surfaces  were 
of  equal  smoothness.  Thus 
the  friction  is  independent  of 
the  area  of  the  rubbing  sur- 
faces. 

FIG<  50.  Put    a    sheet    of    rubber 

upon  one  face  of  A.    Find  w 

by  trial.    It  will  be  quite  different  from  w^    Call  it  wa.     The  friction 

depends  on  the  nature  of  the  rubbing  surfaces. 

The  quotient  — -  is  called  the  coefficient  of  friction  for  the  particu- 
lar surfaces  rubbing.  Thus  ~  =  coefficient  of  friction  of  motion  for 

wood  (of  kinds  used)  on  wood ;  ~  =  coefficient  for  rubber  on  wood, 

etc.  These  coefficients  enable  one  to  find  what  the  friction  would  be 
for  a  given  pressure  between  the  surfaces.  They  are  approximately 
constant  for  any  given  substances. 

The  friction  is  often  stated  to  be  independent  of  the  speed  at 
which  the  surfaces  are  moving  on  each  other.  This  is  by  no  means 
generally  true,  but  for  some  substances  is  nearly  so  where  the  speeds 
change  but  little  from  a  given  amount. 

All  three  of  the  above  laws  are  only  rough  approxima- 
tions. Friction  varies  so  greatly,  with  slight  differences  of 
condition  of  the  surfaces,  that  measurement  of  it  appears 
inexact  and  unsatisfactory. 

Friction  of  Repose. — Adjust  the  load  in  the  pan  until 
it  is  just  sufficient  to  start  A  from  a  state  of  rest.  You  will 
then  find  it  decidedly  greater  than  that  necessary  to  main- 
tain motion.  Here  we  have  the  Friction  of  Repose,  or,  more 


FRICTION  OF  GASES  AND  LIQUIDS. 

properly,  Starting  Friction.  It  varies  with  the  substance, 
the  time  during  which  the  surfaces  have  been  in  contact, 
and  many  other  conditions. 

Friction  of  Gases  and  Liquids. — Lay  a  clean  plate 
of  glass  on  the  table.  Place  upon  it  another  plate  of  about 
the  same  size.  Press  the  two  firmly  together  for  a  mo- 
ment. Then  let  go,  and  slide  the  upper  plate  over  the  lower 
by  pushing  horizontally  against  the  edge  with  your  finger. 
Bear  in  mind  how  hard  you  have  to  push.  Lift  off  the 
upper  plate,  lay  it  gently  down  again  on  the  under  plate, 
and  immediately  slide  it  by  a  side  push.  Note  how  much 
more  easily  it  slides.  This  is  because  the  glass  surfaces  are 
not  so  nearly  in  contact  as  before,  but  are  kept  apart  by  the 
film  of  air  between  them ;  and  the  friction  is  that  of  the 
layers  of  air  parallel  to  the  plates  moving  over  each  other. 
Such  friction  is  much  smaller  in  amount  than  the  solid-sur- 
face friction.  When  the  upper  plate  settles  down  by  its 
weight,  forcing  the  air  out,  the  friction  increases. 

Remove  the  upper  plate,  and  apply  a  layer  of  water  or  oil 
to  the  lower  one.  Put  the  plate  on  again  lightly,  and  notice 
how  easily  it  slides.  Here  the  friction  is  that  of  layers  of 
water  or  oil  parallel  to  the  plates.  The  friction  of  some 
liquids  is  less  than  that  of  others,  and  the  same  is  true  for 
gases ;  in  all  cases,  it  varies  with  temperature. 

The  use  of  oil  for  greasing  or  "lubricating"  rubbing  surfaces 
(axles,  bearings,  etc.)  is  familiar  to  you,  and  is  simply  a  process  of  mak- 
ing the  lesser  friction  of  the  oil  or  other  lubricant  replace  the  greater 
friction  of  the  dry  surfaces.  The  object  is  to  avoid  the  injury  to  the 
surfaces  by  the  grinding  and  polishing  of  the  dry  rubbing,  and  also  to 
do  away  with  the  waste  of  energy  required  to  overcome  such  friction. 

QUESTIONS. — Give  examples  of  friction.  Show  what  the  nature  of  frictional  re- 
sistance is.  Into  what  form  is  the  energy  used  in  overcoming  friction  changed  ? 
Explain  how  this  transformation  is  made.  If  rubbing  surfaces  could  be  made 
perfectly  smooth,  would  there  be  any  friction  ?  Why  ?  State  the  laws  of  slid- 
ing friction.  Describe  a  method  of  proving  each. 

What  is  meant  by  the  coefficient  of  friction  of  motion  ?    If  a  pull  of  5  pounds  is 


142  MACHINES. 

required  to  keep  a  body  just  moving  over  a  horizontal  surface,  the  weight  of 
the  body  being  25  pounds,  what  is  the.  coefficient  of  friction  of  motion  ? 

If  the  coefficient  of  friction  of  motion  of  wood  on  wood  is  0-3,  what  force  would  be 
necessary  to  draw  a  body  weighing  50  pounds  along  a  horizontal  surface  ? 

If  a  force  of  2'1  pounds  was  found  necessary  to  draw  a  block  of  wood  over  a  sur- 
face where  the  coefficient  was  0'3,  what  was  the  weight  of  the  block  ? 

Is  friction  independent  of  the  speed  of  motion  ?  How  may  the  friction  of  gases 
and  of  liquids  be  experimentally  illustrated  ?  Explain  the  action  of  oil  and 
other  lubricants.  What  is  their  object  ? 


MECHANICS.— THE  SIMPLE  MACHINES. 

Mechanics,  in  the  strict  sense  of  the  word,  is  the  Sci- 
ence of  Machines  and  the  art  of  constructing  them.  It  is 
quite  common,  however,  to  include  under  this  head  all  the 
earlier  portions  of  physics,  as  far  as  the  special  branches  of 
Heat,  Light,  Sound,  etc. 

Machines. — Any  apparatus  or  instrument  designed  to 
transform  or  transmit  energy  for  the  purpose  of  doing 
desired  work  is  called  a  Machine. 

Suppose,  for  example,  that  we  have  a  supply  of  coal,  and  wish  to 
move  a  train  of  cars  from  Boston  to  New  York.  The  coal  represents 
a  certain  amount  of  heat-energy,  which  can  be  obtained  by  burning  it. 
In  order  to  move  the  train  the  required  distance,  it  is  necessary  that  a 
certain  amount  of  work  shall  be  done.  The  mere  production  of  the 
heat-energy  by  burning  the  coal  will  not  move  the  train.  How,  then, 
can  the  object  in  view  be  accomplished  I  One  method  is  by  the  use  of 
a  steam  locomotive.  This  takes  up  the  heat-energy  of  the  coal,  and, 
by  various  processes  and  contrivances,  transforms  it  into  mechanical 
energy,  applied  to  its  wheels  in  such  a  way  as  to  perform  the  desired 
work.  The  locomotive,  then,  is  an  example  of  a  machine. 

Machines  are  of  various  degrees  of  complexity, 

from  that  of  a  simple  wooden  rod  or  knife-blade  to  that  of 
the  most  intricate  loom.  In  our  early  experiments,  where 
one  ball  was  made  to  impart  energy  to  another  by  collision 
(page  31),  there  was  no  necessity  for  the  intervention  of  a 
machine,  because  the  mere  collision  of  the  elastic  balls 
served  to  bring  about  the  transference  of  the  energy.  But 
suppose  the  ball  A  had  been  moving  away  from  B,  or  in 


EFFICIENCY  OF  MACHINES. 

some  direction  in  which  it  would  not  strike  B;  then,  to 
transfer  the  energy  from  A  to  B,  we  should  have  required 
some  apparatus  through  which  such  energy  could  be  trans- 
mitted. For  example,  the  balls  might  have  been  connected 
by  a  rope  passing  over  a  wheel  in  such  a  way  as  to  make  B 
move  in  the  desired  direction.  Then  this  rope  and  wheel 
would  have  constituted  a  very  simple  machine. 

Where  the  energy  is  to  be  changed  in  form,  instead  of  being  merely 
transferred,  the  machine  becomes  somewhat  more  complicated,  as  where 
heat-energy  is  to  be  transformed  into  mechanical  energy  in  a  steam- 
engine  (page  286),  or  mechanical  into  electrical  energy  in  a  dynamo- 
electric  machine  (page  522).  But  the  complication  of  machines  arises 
chiefly  from  the  complexity  of  the  kind  of  work  to  be  done,  or  the  per- 
fection with  which  it  must  be  done,  rather  than  from  the  nature  of  the 
process  of  transformation. 

Whatever  its  form,  and  however  perfect  or  complex  it 
may  be,  a  machine  merely  transfers  and  transforms,  but 
can  never  generate,  energy.  In  other  words,  the  work  done, 
or  energy  given  out,  can  never  be  more  than  the  energy 
taken  up  by  the  machine. 

Efficiency  of  Machines. — An  ideal  machine  would 
give  out  as  useful  work  all  the  energy  applied  to  it.  In 
practice,  owing  to  friction,  bending,  and  certain  laws  of  the 
availability  of  energy,  no  machine  is  ideal.  Actual  ma- 
chines, then,  give  out  less  useful  work  than  is  equivalent  to 
the  energy  imparted  to  them.  The  "  lost "  energy  is  merely 
changed  within  the  machine  into  forms  which  are  not  of 
service  for  the  purpose  of  the  machine.  Thus,  friction 
causes  some  energy  to  be  transformed  into  useless  heat,  and 
is  one  of  the  chief  sources  of  loss  in  most  machines. 

The  ratio  of  the  amount  of  useful  work  given  out  by  the 
machine  to  the  total  energy  put  into  it  is  called  the  efficiency 
of  the  machine.  For  instance,  if  a  certain  machine  had 
applied  to  it  10  foot-pounds  of  energy,  and,  owing  to  fric- 
tion, converted  2  foot-pounds  into  heat,  and  wasted  1  foot- 
pound in  other  ways,  it  could  give  out  only  7  foot-pounds. 


144 


MACHINES. 


Its  efficiency  as  a  machine  would  then  be  -fa,  or  70  per 
cent. 

The  Simple  Machines. — There  are  a  few  machines  so 
simple  in  form  and  principle  that  they  are  called  the  Simple 
Machines.  The  more  complicated  machines  are  composed 
largely  of  combinations  and  modifications  of  these.  The 
simple  machines  are  sometimes  called  the  mechanical  pow- 
ers They  are  the  Lever,  Wheel  and  Axle,  Inclined  Plane, 
Wedge,  Screw,  Pulley,  and  Knee. 

In  studying  the  principles  of  these  machines,  we  shall  consider 
them  as  ideal — that  is,  as  if  they  were  without  mass  and  weight,  and 
as  if  they  worked  without  friction,  bending,  etc.  In  actual  practice 
these  things,  of  course,  do  exist,  and  must  be  taken  into  account,  but 
they  do  not  affect  the  principles  of  the  machines. 

The  Lever. — To  move  heavy  objects,  such  as  rocks,  etc., 
the  workman  uses  a  crow-bar  or  pry.  This  is  a  bar  or  rod, 

usually  of  iron. 
One  end  of  the  bar 
is  placed  under  the 
rock  to  be  moved, 
as  at  B  (Fig.  51). 
Beneath  this  end, 
at  F,  is  set  a  stone 
or  other  small  ob- 
ject, and  then  the 
workman  presses 
down  at  A  with 
his  hand  or  by 
bearing  on  with 
the  weight  of  his 
body.  By  this  means  he  is  able,  with  a  comparatively  small 
force  applied  at  A,  to  lift  a  very  heavy  object  at  B.  A  bar 
so  used  is  one  form  of  Lever. 

EXPERIMENTS  WITH  THE  LEVER. — Obtain  a  strong  stick  five  or  six 
feet  long,  or  a  crow-bar,  and  try  to  move  a  heavy  object  as  shown  in 
Pig.  51.  Put  F  at  first  half-way  from  A  to  B,  and  notice  the  pressure 


FIG.  51. — ILLUSTRATING  THE  ACTION  OP  THE  CROW 
BAR. 


THE  LEVER, 


145 


required  at  P  to  lift  D  or  to  tip  it  up.  Place  F  nearer  and  nearer  to 
B,  and  observe  how  the  force  required  at  P  is  less  and  less  as  A  F  be- 
comes greater  in  proportion  to  B  F.  You  will  be  surprised  at  the 
amount  you  can  lift  by  making  B  F  very  short  in  proportion  to  A  F. 
Your  bar  is  a  true  lever. 

The  force  P  at  A  will  be  called  the  working  force  or  the 
power,  The  force  L  at  B  will  be  called  the  load.  The 
point  F  of  support,  in  other  words  the  pivot,  will  be  called 
the  fulcrum.  In  principle,  a  Lever  is  any  solid  pivoted 
rod  by  means  of  which  a  force  at  one  point  is  made  to  bal- 
ance a  load  at  another  point. 

Kinds  of  Levers. — Levers  are  generally  classed  as  of 
three  "  orders  "  ;  but  this  classification  is  of  no  special  im- 
portance, since  the  law  is  the  same  for  all.  The  first  order 
(Fig.  52)  is  where  the  fulcrum  is  be-  F 

tween  the  two  forces  (power  P  and 
load  L) ;  the  second,  where  the  load 
is  between  the  power  and  the  ful- 
crum ;  the  third,  where  the  power  is 
between  the  load  and  the  fulcrum. 


Y3 


A  2 


As  an  aid  to  the  memory,  observe  that 
in  the  three  orders  the  initial  letters  F  L  P 
of  the  middle  points — fulcrum  (1),  load  (2), 
power  (3)— stand  in  alphabetical  order. 

The  Principle  of  the  Lever. — 

In  Fig.  52,  for  each  order,  we  have 
the  power  P  working  at  A,  the  load 
L  at  B,  and  the  fulcrum  at  F.  The 
arrows  represent  the  amount  and  di- 
rections of  the  forces  L  and  P,  and 
the  pressure  on  the  fulcrum  F,  start- 
ing with  the  same  load  L  in  all  cases, 
and  with  P  and  L  at  right  angles  to  the  lever,  which  is 
represented  as  straight  and  horizontal  for  simplicity. 

We  have,  then,  in  each  case  two  forces,  P  and  L,  tending 


FIG.  52.— THREE  ORDERS 
LEVERS. 


146  MACHINES. 

to  turn  the  lever  about  the  fulcrum  F.  The  moment  of  the 
power  is  Px  A  F,  that  of  the  load  is  LxB  F.  For  equilib- 
rium, these  two  moments  must  be  equal  and  must  be  in  oppo- 
site directions  (page  112).  Hence,  to  balance  a  given  load  L 

on  a  lever,  we  must  have  Px  A  F  =  Lx  B  F  or  P  — '  =  L. 

B  F 
AF 
The  ratio  ^  is  called  the  leverage.     The  law  of  the  lever 

may  be  stated  thus : 

For  equilibrium  on  a  lever,  the  moment  of  the  power 
must  be  equal  and  opposite  to  the  moment  of  the  load.  Or 
the  poiver  into  the  leverage  must  equal  the  load,  and  the 
direction  of  the  moments  must  be  opposite. 

ILLUSTRATIVE  EXAMPLES. — A  man  wishes  to  raise  a  stone  Weighing 
a  ton.  He  uses  a  horizontal  lever  of  the  first  order,  and  is  able  to  make 
the  distance  from  power  to  fulcrum  4  feet,  and  that  of  load  to  fulcrum 
6  inches.  How  much  force  must  he  exert  at  P  ?  PxAF  =  LxBF 

/.  P  x  4  =  2000  x  0-5  .-.  P  =  200°4xQ'5  =  250  pounds. 

What  was  his  leverage  I    4^=^4  =  8. 
J3  Jb     0*5 

Suppose  he  weighs  150  pounds,  could  he  lift  the  rock  by  his 
weight  with  this  leverage  ?  No  ;  because  he  requires  250  pounds,  and 
can  obtain  only  150  pounds.  Of  course,  he  might  add  to  this  weight 
by  using  other  rocks. 

What  leverage  must  he  have  to  be  able  just  to  balance  the  rock  ? 

2000 

P  x  leverage  =  L  .-.  150  x  leverage  =  2000  .-.  leverage  =  £~  =  13-3. 

150 

If,  then,  his  lever  is  4-5  feet  long,  where  must  the  fulcrum  be 
placed*  ^  =  13.3,^™=!2i±^.  B«tAF  +  BP  = 

4.5 

whole  length  of  lever  =  4-5  feet .'.  B  F  =^r3  =  0-31  ft.  or  3-7  inches 
/.  A  F  -  4-5  -  0-31  =  4-2  feet, 

Pressure  on  the  Fulcrum. — In  the  lever  there  must 
always  be  a  pressure  on  the  fulcrum.  If  the  power  and  load 
are  parallel,  as  in  Fig.  52,  the  pressure  on  F  will  be  found  by 
the  laws  for  the  resultant  of  parallel  forces.  If  P  and  L  are 


COMMON  FORMS  OF  THE  LEVER. 


147 


not  parallel,  the  pressure  on  F 
must  be  found  by  the  paral- 
lelogram of  forces. 


DA-. 


FIG.  53.— POWER  APPLIED 
OBLIQUELY. 


Oblique  Forces  and  Bent 
Levers. — If  the  lever  is  straight, 
but  either  P  or  L  is  not  at  right 
angles  to  it,  then  the  moment 
must  be  found  by  dropping  a  perpendicular  from  F  upon 
its  line  of  action.  For  instance,  in  Fig.  53,  equilibrium 

would    occur    only   when 


In  general  the  lever  is  not 
straight,  but  curved  or  angu- 
lar.   This  makes  no  difference 
in  its  principle.     The    truck 
(Fig.  54)  is  a  form  of  lever ;  the 
fulcrum  is  the  axle  of  the  wheels,  and 
the  moments  are  P  x  F  C  and  L  x  F  D, 
which  must  be  equal  and  opposite.    A 
form  of  bent  lever  which  has  many 
important  applications  is  called  the 
"  bell-crank  lever "  because  of  its  fa- 
miliar use  to  turn  corners  in  bell-wires 
in  houses.     Find  one,  make  a  drawing 
of  it,  and  explain  its  principle. 

Among  the  common  forms  of  the 
lever  may  be  mentioned  the  pump-handle,  well-sweep,  shears  and  scis- 
sors, claw-hammer  when  used  to  draw  nails,  walking-beam  of  steam- 
boat,   oar,    forceps,    tongs,   the 
steelyard,  and  all  movable  bones 
of  the  bodies  of   men  and  ani- 
mals. Explain  from  Fig.  55  how 
the  forearm  acts  as  a  lever  when 
raising  a  weight   in   the   hand. 
To  what  order  does  it  belong  ? 

Work  done  with  Le- 
ver.— Take,  as  an  example, 

a    lever    Of    the     first    kind,  FIG.  55.— THE  FOREARM  A  LEVER. 


FIG.  54.— THE  HAND-TRUCK. 


148  MACHINES. 

A  B  (Fig.  56),  and  suppose  P  and  L  to  remain  always  at 
right  angles  to  the  lever  as  it  moves.  If  the  end  A  be 

moved  by  P  until  it  has  passed 

£      P  A       on  to  any  point  C,  it  will  have 

3  j       passed  through  a  distance  A  C 

~"~~— --.Jc      along  the  arc  of  a  circle  with 

Flo.  56.  F  as  a  center.     The   end  B 

will  at  the  same  time  pass 

through  a  distance  B  D  along  another  arc  whose  center 
is  also  at  F.  By  geometry,  AC:BD  =  AF:BF.  But, 
by  the  law  of  the  lever,  A  F  :  B  F  =  L  :  P  .-.  A  C  :  B  D 
=  L  :  P  .-.  Fx  A  C  =  LxB  D.  But,  as  shown  on  page  97, 
work  is  the  product  of  the  force  into  the  distance  through 
which  the  body  moves  ;  therefore  P  X  A  C  =  work  done  by 
P,  and  L  X  A  F  =  work  done  against  L.  Hence,  the  work 
done  upon  the  lever  by  the  working  energy  is  equal  to  the 
work  done  by  the  lever  against  the  load. 

This  fact  is  also  a  necessary  and  direct  consequence  of  the  princi- 
ple of  the  conservation  of  energy.  The  law  of  the  lever  might  equally 
well  be  deduced  by  assuming  that  principle  and  working  backward 
from  it,  as  will  be  done  in  the  case  of  some  other  machines. 

Actual  Lever. — The  demonstrations  have  shown  the 
principle  of  the  ideal  lever.  In  the  actual  lever  we  must 
allow  for  the  mass  and  weight  of  the  lever,  for  friction,  for 
the  fact  that  in  most  cases  the  forces  change  direction  and 
therefore  leverage  as  the  lever  moves,  and,  finally,  for  the 
energy  required  to  set  in  motion  the  object  moved. 

Perpetual  Motion. — It  has  been  stated  that  no  ma- 
chine can  give  out  more  energy  than  is  put  into  it ;  or,  in 
other  words,  can  do  more  work  than  is  done  upon  it — this 
being  a  necessary  consequence  of  the  principle  of  conserva- 
tion of  energy.  If  any  machine  could  give  out  more  energy 
than  it  received,  then  of  that  energy  a  part  might  be  utilized 
to  run  the  machine  itself,  and  the  rest  stored  up  for  future 
use.  Thus  the  machine  could  keep  itself  going,  and  at  the 


MECHANICAL  ADVANTAGE.  149 

same  time  supply  energy.  This  would  manifestly  imply  a 
generation  of  energy ;  but  we  have  proof  on  every  hand  that 
energy  can  not  be  generated,  and  the  supposed  case  must, 
therefore,  be  an  impossibility.  Even  a  machine  which  will 
keep  itself  running  without  any  outside  supply  of  energy  is 
also  an  impossibility,  because  it  is  physically  impossible  that 
there  should  not  be  some  energy  wasted — i.  e.,  turned  into  un- 
available forms — in  every  machine.  Hence  a  machine  with 
an  efficiency  of  unity,  or  one  hundred  per  cent,  is  impossi- 
ble. Such  machines  are  commonly  spoken  of  as  perpetual- 
motion  machines,  obviously  because  they  could  keep  them- 
selves going  perpetually. 

Schemes  for  perpetual-motion  machines,  and  for  machines  that 
would  produce  more  energy  than  was  required  to  run  them,  were  much 
more  common  before  the  doctrine  of  energy  was  well  understood  than 
at  present.  That  "  you  can  not  make  something  out  of  nothing,"  is  as 
true  of  energy  as  of  matter. 

Mechanical  Advantage. — Although  there  can  be  no 
gain  of  energy  by  any  machine,  but  must  always  be  more  or 
less  actual  loss,  yet  there  may  be  a  great  advantage  derived 
from  its  use.  We  are  able  to  accomplish  things  with  the 
aid  of  machines  which  we  could  not  do  without  them,  be- 
cause the  machines  enable  the  energy  at  our  command  to 
do  work  for  which  it  would  not  be  available  if  directly 
applied. 

Take,  for  example,  the  lever.  Suppose  that  a  man  who  can  lift 
only  100  pounds  wishes  to  raise  a  rock  weighing  1,000  pounds.  It  is 
ten  times  as  much  as  he  can  possibly  lift.  He  has  energy  enough  to 
lift  the  rock  to  any  desired  height,  for  if  the  rock  were  in  ten  equal 
parts  he  could  lift  each  separately  to  that  height,  thus  doing  the  work, 
and  the  mere  separation  of  the  rock  into  parts  has  not  increased  his 
energy.  But  he  can  not  exert  force  enough  to  lift  the  rock  as  a  whole 
against  gravity — that  is,  he  can  not  exert  force  enough  to  balance  the 
weight  of  the  rock.  Give  him  a  lever,  however,  with  a  leverage  of  10 
to  1,  and  he  can,  by  exerting  100  pounds  on  the  long  end,  produce 
1,000  pounds  at  the  short  end.  and  thus  balance  the  weight  of  the  rock. 
Then,  by  keeping  up  the  pushing  (ten  times  as  far  as  the  load  moves) 


150  MACHINES. 

}ie  can  perform  the  work  necessary  to  lift  the  rock  to  the  desired 
height,  doing  no  more  work  than  that  required  to  lift  the  ten  separate 
parts.  It  is  thus  apparent  that,  although  he  has  gained  no  energy, 
the  lever  has  made  his  energy  available  for  the  purpose  at  hand,  and 
therein  is  the  "  advantage."  An  advantage  thus  gained  by  means  of 
a  machine  is  called  a  Mechanical  Advantage. 

Think  over  the  various  forms  of  lever  and  of  other  machines  as 
you  come  to  them,  and  see  wherein  the  mechanical  advantage  consists, 
and  how  there  is  no  gain,  but  rather  some  loss  of  energy.  This  is  the 
key  to  the  intelligent  understanding  of  all  machines. 


QUESTIONS.— What  is  meant  by  the  term  Mechanics  in  its  strict  sense  ?  How  is  it 
quite  commonly  employed  ?  What  is  a  Machine  ?  Give  examples.  Why  do 
we  have  to  use  machines  ?  Can  machines  generate  energy  ?  If  not,  of  what 
use  are  they  ?  How  can  we  generate  energy  ?  What  is  meant  by  an  ideal  ma- 
chine I  Why  must  any  actual  machine  be  inferior  to  an  ideal  machine  ?  What 
becomes  of  energy  wasted  by  a  machine  ?  In  what  way  is  much  of  the  wasted 
energy  used  up  ?  What  is  meant  by  the  efficiency  of  a  machine  ? 

A  certain  machine  gives  out  as  useful  work  two  thirds  of  the  energy  applied  to 
it ;  what  is  its  efficiency  ?  A  certain  machine  wastes  one  quarter  of  the  energy 
applied  to  it ;  what  is  its  efficiency  ? 

What  is  meant  by  the  '"  simple  machines  "  ?  Name  those  described  in  this  chap- 
ter. Why  do  we  consider  first  ideal  machines  in  studying  the  laws  and  princi- 
ples of  the  simple  machine  ? 

Describe  the  Lever.  What  is  meant  by  the  power  ?  the  load  ?  the  fulcrum  ?  De- 
scribe the  three  orders  of  lever.  State  the  rule  or  law  of  the  lever.  Deduce 
this  law.  Define  leverage. 

A  man  wishes  to  pull  upward  on  a  chain  with  a  force  of  500  pounds,  and  has  a 
horizontal  lever  of  the  first  order  11  feet  long  ;  what  pressure  must  he  use  if  he 
places  the  fulcrum  one  foot  from  the  load  ?  What  would  then  be  his  leverage  ? 
If  he  can  use  but  25  pounds  pressure,  what  leverage  must  he  have  ?  Where 
must  the  fulcrum  be  placed  ?  Solve  the  same  problems  with  the  lever  of  the 
second  order.  In  the  first  problem,  how  much  would  be  the  pressure  on  the 
fulcrum  ?  Suppose  that  the  man  pressed  at  an  angle  of  45°  to  the  lever  instead 
of  at  right  angles  to  it,  how  much  pressure  must  he  exert  ?  Suppose  that  both 
power  and  weight  were  vertical,  but  that  the  lever  was  inclined  at  45°  to  the 
horizontal,  how  much  pressure  would  be  required  ?  Why  is  it  usually  best  to 
push  as  nearly  at  right  angles  to  the  lever  as  possible  ? 

What  is  the  relation  between  the  work  done  upon  and  by  an  ideal  lever  ?  Be- 
tween the  energy  put  into  it  and  that  given  out  ?  Deduce  the  law  of  the  lever, 
starting  with  the  principle  of  the  conservation  of  energy.  If,  in  the  first  prob- 
lem with  the  lever,  the  man  was  obliged  to  put  in  one  half  as  much  more  work 
on  account  of  friction  as  was  necessary  to  balance  the  load,  how  much  must  he 
increase  the  moment  of  the  power  ?  If  the  leverage  is  kept  tne  same,  what 
pressure  must  he  exert  ?  If  the  pressure  is  kept  the  same,  how  much  must  he 
increase  the  leverage  ?  What  would  be  the  efficiency  of  this  lever  ?  Show  how 
each  of  the  examples  mentioned  on  page  147  is  a  lever,  and  of  what  order. 

If  a  machine  could  give  out  110  foot-pounds  for  every  IOC  foot-pounds  supplied, 
what  would  be  its  efficiency  ?  Would  such  a  machine  be  possible  ?  What  would 


THE  WHEEL  AND  AXLE. 


151 


it  be  called  ?  Why  ?  If  possible,  would  such  a  machine  be  valuable  ?  Why  ? 
How  do  we  know  that  such  a  thing  is  impossible  ?  What  is  meant  by  mechan- 
ical advantage  ?  Give  an  example. 


WHEEL  AND  AXLE.— INCLINED  PLANE.— WEDGE. 

Wheel  and  Axle. — Let  C  represent  a  wheel  around 
which  is  wound  a  cord  carrying  a  weight  P.  Let  E  D 
represent  the  axle  to  which  C  is  fastened,  turning  in  the 
supports.  A  side  view  is  shown  at  A  B  F,  on  the  right. 


FIG.  57.— PRINCIPLE  OP  THE  WHEEL  AND  AXLE. 

Around  the  axle  is  wound  a  rope  at  G,  carrying  a  larger 
weight  L.  In  this  machine,  P  is  the  power  and  L  the  load, 
just  as  in  the  lever ;  by  examining  closely  you  will  see  that 
the  wheel  and  axle  is  merely  a  modification  of  the  lever. 
The  fulcrum  is  at  F,  the  axis  of  rotation ;  the  power  is  ap- 
plied at  A,  at  the  end  of  a  lever-arm  A  F;  the  load  at  B, 
at  the  end  of  a  lever-arm  B  F.  The  moment  of  the  power 
is  PxA  F;  of  the  load,  LxB  F.  As  the  power  descends 
the  cord  unwinds,  and  P  thus  acts  always  with  a  constant 
arm.  Similarly,  as  P  descends  L  ascends,  the  rope  winds 
up,  and  L  acts  always  with  a  constant  lever-arm  B  F. 

The  wheel  and  axle  is  merely  a  device  for  making  the 
lever  continuous  in  its  operation.  The  laws  in  the  case  of 
this  machine  are  the  same  as  those  of  the  lever. 

Modifications  of  the  Wheel  and  Axle.— The  wheel 
is  often  replaced  by  a  crank,  the  power  being  applied  to  the 


152 


MACHINES. 


handle  of  the  crank,  either  by  hand  or  by  machinery.  Such 
a  device  is  often  used  for  raising  a  bucket  of  water  from  a 
well ;  and  most  hoisting  apparatus,  as  cranes,  derricks,  etc., 

are  further  modifications  of  the 
wheel  and  axle,  as  are  also  the 
capstan,  the  pilot-wheel,  and 
the  windlass. 

Gear-wheels  act  on  the  same 
principle.  In  Fig.  58  the  hand 
represents  the  power  pulling  a 

f*i  cord  upon  the  circumference  of 

'  J  J  i          a  wheel.     On  the  axle  is  a  small 

/  Jj          toothed  wheel  which  "  meshes " 

FIG.  58,-TRAiN  OF  WHEELS  m  GEAR.     *nto  a  larger  one.    This  in  turn 

carries   a   small  one  engaging 

with  a  larger  wheel,  and  so  on.  The  second  large  wheel 
turns  more  slowly  than  the  first ;  the  third,  more  slowly 
than  the  second.  Thus  the  load  winds  up  on  the  axle  of 
the  third  wheel  much  more  slowly  than  the  power  descends. 
Such  an  arrangement  is  called  a  train  of  wheels. 

Suppose  that  the  power  descends  10  inches  while  the  load  rises  1 
inch ;  then  P  x  10  =  L  x  1,  and  L  =  10  P — that  is,  the  power  can  bal- 
ance ten  times  itself.     In  general,  let  a  denote  the  distance  through 
which  the  power  moves,  and  b 
the  distance  through  which  the 
load  moves  in  the  same  time; 
then  P  x  a  =  L  x  b. 

Another  modification  of  the 
wheel  and  axle  occurs  in  the 
transmission  of  power  by  belt- 
ing. Let  A  C  represent  a  large 
pulley  running  on  a  shaft  G, 

and  I)  F  a  small  pulley  running  on  a  shaft  H.  The  belt  is  continuous, 
and,  starting  from  A,  passes  around  B  C  D  E  F  back  to  A.  If  the  cir- 
cumference of  A  C  is  twice  that  of  D  F,  and  the  former  drives  the  lat- 
ter, then  D  F  must  turn  twice  as  many  times  a  minute  as  A  C.  Any 
other  pulley  attached  to  the  shaft  H  would  also  turn  twice  as  fast  as 
A  C.  A  large  pulley  on  this  shaft  might  be  belted  to  a  small  one  on 


FIG.  59.— ILLUSTRATING  THE  BAND. 


THE  INCLINED  PLANE. 


153 


another  shaft,  which  would  then  move  still  faster.     The  same  arrange- 
ment may  be  used  in  reverse  order  to  reduce  speed. 

Inclined  Plane. — Any  flat  surface  which  is  not  hori- 
zontal forms  an  Inclined  Plane.  A  flat  board  more  or  less 
tipped,  a  "  pitched  "  roof,  a  smooth  hill-side,  a  grade  on  a 
road  or  railway,  the  sloping  surface  of  a  sand-bank,  are 
examples  of  inclined  surfaces  more  or  less  approaching  to 
perfect  inclined  planes.  In  machinery,  we  find  inclined 
planes  in  modified  forms  in  the  eccentric,  cam,  wedge, 
screw,  propeller-blade,  windmill  fan,  etc. 

The  amount  of  inclination  of  the  plane  is  called  its  grade 
or  slope,  and  is  measured  by  the  amount  that  the  plane  rises 
from  a  level  in  a  given  horizontal  distance,  or  by  the  ratio 
of  the  rise  to  the  horizontal  distance.  For  instance,  if  a 
road  has  such  a  steepness  that  it  rises  5  feet  vertically  in  a 
distance  of  100  feet  horizontally,  then  its  grade  or  slope  is 
said  to  be  5  feet  in  100  feet,  or  simply  5  in  100,  or  5  per 
cent.  The  grade  may  also  be  expressed  by  the  angle  (meas- 
ured in  degrees)  between  the  surface  and  the  horizontal. 

Let  A  B  represent  the  board  of  the  apparatus  of  page  78,  supported 
in  an  inclined  position  by  an  upright.  Then  the  grade  or  slope  of  the 
inclined  plane  A 
B  would  be  the 
amount  d  e  that 
the  board  rises  in 
a  horizontal  dis- 
tance a  e,  or  the 
ratio  d  e  :  a  e.  If 
d  e  =  2  feet  and 
a  e  =  5  feet,  then 
the  grade  is  2  feet 
in  5,  or  4  in  10,  or 
40  per  cent. 

Suppose     the 
cart  to  be  placed 
in     the     position 
shown  in  Fig.  60,  and  loaded 
load,  equal  to  10  pounds. 
11 


FIG.  60.— INCLINED  PLANE. 


as  to  make  W,  the  weight  of  cart  and 
This  weight  may,  for  present  purposes,  be 


154  MACHINES. 

considered  as  acting  vertically  downward  through  the  center  of  mass, 
g,  of  cart  and  load.  Let  g  h  represent  this  weight.  Draw  through  g 
the  lines  g  i  parallel  to  the  plane  and  g  j  perpendicular  to  it.  Resolve 
the  force  W  into  components  in  these  two  directions,  by  completing 
through  h  the  parallelogram.  Then  the  two  forces,  g  i  and  gj,  will  be 
equivalent  in  effect  to  W.  Thus,  owing  to  the  weight,  there  is  a  force 
represented  in  amount  and  direction  by  g  i  pulling  the  cart  downward 
along  the  plane,  and  another  simultaneous  force,  gj,  perpendicular  to 
the  plane.  The  force  gj  can  not  result  in  motion,  since  it  is  wholly 
counterbalanced  by  the  resisting  pressure  of  the  plane.  The  force  g  i 
will  produce  motion  down  the  plane,  unless  counterbalanced.  The  cart 
will,  therefore,  run  down  the  plane.  But  notice  that  the  force  g  i  is 
less  than  W ;  hence  the  acceleration  down  the  plane  will  be  much  less 
than  if  the  cart  were  allowed  to  fall  freely  in  a  vertical  direction. 

To  hold  the  cart  in  equilibrium  we  must,  then,  apply  a  pull  along 
the  cord  in  amount  equal  to  g  i.  Observe  that,  if  the  grade  is  made 
greater,  the  amount  of  g  i  will  be  greater  for  the  same  load  W ;  hence 
g  i  increases  as  the  grade  increases.  A  horse  pulling  a  wagon  up  a 
hill  has  to  pull  with  more  force  as  the  slope  grows  steeper. 

The  Friction  of  any  Body  moving  over  a  Surface 

is  proportional  to  the  pressure  against  the  surface.  Notice 
that  gj  diminishes  as  the  pitch  increases,  and  is  always  less 
than  W.  Hence,  the  steeper  the  pitch,  the  less  the  work 
against  friction. 

To  pull  the  Cart  up  the  Plane,  then,  by  a  force  par- 
allel to  the  plane,  we  must  apply  energy  at  a  sufficient  rate 
to  produce,  first,  force  enough  to  balance  the  backward  pull 
g..i,  and,  in  addition,  enough  more  force  to  do  the  work  of 
friction  necessary  to  move  the  cart  at  the  desired  speed,  and 
also  to  accelerate  the  cart  if  it  is  to  be  started  from  rest  or 
is  to  be  moved  with  accelerated  motion.  This  is  the  energy 
supplied  by  an  engine  drawing  a  train  up  a  grade,  or  by  a 
person  in  walking  up-hill. 

Work  on  Inclined  Plane.  —  Force  parallel  to 
Length. — Suppose  the  cart  to  be  pulled  up  the  length 
ad  of  the  plane  by  a  force  P  parallel  to  ad.  The  work 
performed  by  the  energy  which  produces  the  force  P  will  be 


ANGLE   OF  REPOSE.  155 

measured  by  P  X  ad.  The  work  done  upon  the  cart,  if  fric- 
tion be  neglected,  consists  in  raising  it  through  a  distance 
equal  to  e  d  against  the  resistance  W  of  its  weight,  and  is 
therefore  Wxed.  These  two  quantities  must  be  equal  to 
each  other  by  the  principle  of  the  conservation  of  energy. 
Therefore  Pxad  =  Wxed,  or  P  :  W  =  ed  :  ad  =  height  : 
length.  This  would  be  the  least  value  of  P  for  a  given 
weight  W. 

In  any  actual  case,  the  work  done  must  be  greater  than  P  x  ad, 
and  therefore  the  actual  working  force  must  be  greater  than  P  by  an 
amount  necessary  to  do  the  work  of  friction,  of  acceleration,  etc. 

Force  parallel  to  Base. — In  its  application  to  ma- 
chinery, the  inclined  plane  is  used  to  raise  or  force  apart 
bodies  or  portions  of  machines.  For  instance,  the  rod  A  B, 
running  in  the  guide  C  D  and  pressing  downward  with  a 
force  F,  may  require  to  be  lifted.  This  may  be  done  by 
forcing  under  it  the  inclined  plane  a  d  e  sliding  on  the  sur- 
face G  H.  Let  the  pressure  be  exerted  by  a  force  P  parallel 
to  the  surface  G  H.  How  great  must  this  force  be  in  order 
to  push  A  B  backward  against  F  ? 

Suppose  the  plane  moved  along  so  that  the  whole  length  a  d  is 
gradually  pushed  under  A  B,  which  will  thus  be  lifted  against  F 
through  a  distance  equal  to  e  d.  The  work 
done  upon  it  will  then  be  F  x  ed.  The 
work  done  by  P  will  be  P  x  ea,  and  this, 
friction  being  neglected,  must  be  just 
equal  to  F  x  ed.  Therefore,  P  x  ea  =  F  x  ed 
.'.  P  :  F  =  ed  :  ea  =  height  :  base.  This 
would  give  the  minimum  value  of  P.  In 
an  actual  machine,  P  would  be  enough 
greater  to  do  the  work  of  friction,  accelera- 
tion, etc.  FIG"  61'  . 

Angle  of  Repose. — If  any  body  is  allowed  to  roll  or 
slide  down  a  grade,  then  gravity  furnishes  the  energy  to 
do  the  work  of  friction  and  acceleration.  In  this  case  it 
will  be  seen  that,  since  friction  is  a  retarding  force,  and  g  i 
diminishes  toward  zero  as  the  pitch  of  the  plane  is  made 


156  MACHINES. 

smaller,  there  will  be  a  certain  pitch  at  which  the  force  g  i 
will  be  just  equal  to  the  friction.  At  this  pitch  the  body 
will  continue  to  roll  or  slide  at  a  uniform  velocity  when 
started,  because  under  balanced  forces  and  therefore  follow- 
ing the  first  law  of  motion.  If  the  angle  is  further  dimin- 
ished, the  force  g  i  will  become  less  than  the  friction,  and 
the  body  if  started  will  soon  stop.  The  angle  at  which  this 
result  is  just  reached  is  called  the  Angle  of  Kepose. 

Pour  sand  slowly  out  of  a  pail  or  beaker  upon  the  table.  It  will 
pile  up  steadily  at  first ;  but  soon  the  slope  of  the  sides  of  the  pile  will 
be  equal  to  the  angle  of  repose  for  sand,  and  any  more  sand  poured 
upon  the  top  will  slip  down  over  the  sides  to  the  foot  of  the  pile,  and 
the  angle  of  the  sides  will  be  maintained  nearly  constant.  Or  build 
up  a  high  pile  of  moist  sand,  and  let  it  dry.  Jar  it  a  little  and  it  will 
begin  to  fall  and  continue  falling  until  the  slope  of  the  sides  is  the 
angle  of  repose  of  the  dry  sand.  For  this  reason,  at  the  foot  of  sand 
or  gravel  banks  and  rocky  cliffs,  the  natural  piles  of  fallen  material 
will  be  seen  to  have  quite  a  uniform  incline.  The  slopes  where  a 
railroad-bed  has  been  constructed  by  filling  in,  or  by  cutting  through 
gravel  or  sand,  illustrate  the  angle  of  repose. 

Experiments  should  be  tried  by  the  pupil  in  measuring 
the  angle  of  repose  for  various  substances,  as  for  blocks  of 
different  material  on  a  board  arranged  to  tip  at  various 
angles ;  for  gravel,  shot,  etc.  The  angle  of  repose  of  water 
is  zero — that  is,  the  surface  of  a  mass  of  water  is  perpendicu- 
lar to  the  line  of  action  of  its  weight,  and  is  therefore  what 
we  call  level ;  yet  the  surface  of  water  is  not  a  plane,  but  a 
part  of  a  sphere  with  its  center  at  the  earth's  center. 

The  Wedge. — Fig.  62  shows  the  Wedge  in  its  simplest 
form.  The  action  here  is  merely 
that  of  the  inclined  plane.  The 
solid  ade  in  Fig.  61  is  really  a 
wedge,  and  its  upper  and  under 
surfaces  are  planes  inclined  to 
each  other.  The  axe,  the  chisel, 
the  knife,  the  diamond  used  in 
.-THE  WEDGE.  glass-cutting,  are  applications  of 


THE  SCREW.  157 

the  principle  of  the  wedge.  The  surfaces  of  the  wedge  may 
be  curved  instead  of  plane,  as  in  the  case  of  the  points  of 
pins  and  needles,  awls,  etc.,  and  the  sharp  edges  of  all  cut- 
ting tools  as  seen  through  a  magnifier. 

The  mechanical  advantage  gained  by  the  wedge  is  greater 
as  its  slope  is  less ;  but  for  cutting  tools  the  slope  has  to  be 
adapted  to  the  materials  to  be  cut,  being  less  for  wood  and 
soft  substances  than  for  iron  and  other  metals. 


QUESTIONS. — Describe  the  Wheel  and  Axle.  Deduce  its  law.  How  is  it  related  to 
the  lever  ?  Give  examples.  If  the  length  of  lever  used  in  a  capstan  is  4  feet 
and  the  drum  is  of  6  inches  radius,  how  much  pull  on  the  rope  would  be  created 
by  a  force  of  50  pounds  on  the  end  of  the  bar  ?  Describe  the  Inclined  Plane. 
Give  examples.  What  is  meant  by  the  grade  or  slope  of  an  inclined  plane  ? 

A  plane  rises  4  feet  in  200  feet.  What  is  its  grade  or  slope  ?  Measure  the  slope 
of  a  d  (Fig.  60).  If  the  weight  W  is  10  pounds,  what  is  the  pull  gi  ?  What  is 
the  pressure  gj  ?  How  much  weight  would  be  required  at  P  to  prevent  the  cart 
from  moving  ? 

A  horse  is  going  up  a  hill  with  a  grade  of  5  feet  in  100,  and  is  drawing  a  load  of  a 
ton.  How  much  force  must  he  pull  with  ?  If  he  has  to  do  10  per  cent  addi- 
tional work  for  friction,  how  much  must  he  pull  ?  If  he  ascends  150  feet  verti- 
cally, how  much  work  must  he  do,  B.  E.  U.  ?  If  the  grade  is  twice  as  great, 
how  much  must  he  pull  ? 

Measure  the  slope  of  the  plane  ad  in  Fig.  61.  How  much  of  a  load  on  A  can  a 
force  of  100  pounds  at  P  balance  ? 

What  is  meant  by  the  angle  of  repose  ?    Give  examples. 

What  is  the  Wedge  ?  Give  illustrations.  How  does  the  mechanical  advantage 
of  the  wedge  depend  upon  its  slope  ? 


SCREW.— PULLEY.— BALANCE. 

The  Screw  is  one  of  the  most  important  modifications 
of  the  inclined  plane.  Let  A  B  (Fig.  63)  represent  a  solid, 
circular  cylinder  of  metal  or  wood.  Let  0  D  E  F  be  a  sheet 
of  paper  cut  so  that  C  D  is  perpendicular  to  D  E,  and  0  F 
slopes  by  any  suitable  amount.  The  paper  will  then  illus- 
trate the  side  view  of  an  inclined  plane  as  in  Figs.  60  and  61. 
Fasten  this  on  the  cylinder  with  C  D  parallel  to  its  axis,  and 
then  wrap  the  paper  around  the  cylinder.  The  edge  C  Gr  F 
will  wind  itself  up  as  a  spiral  line  around  the  cylinder,  as 
shown  in  the  dotted  lines  Gr,  H,  I,  etc. 


158 


MACHINES. 


FIG.  63.— PRINCIPLE  OF  THE  SCREW. 


Examine  the  figure  A'  B',  which  is  the  side  view  of  a 
square-threaded  screw;  or,  better  still,  examine  an  actual 

screw.  You  will  see  that 
the  lines  G'  K,  H'  L,  1'  M 
of  the  threads  of  the  screw 
correspond  to  the  lines  G, 
H,  I,  etc.  The  upper  and 
also  the  under  surface  of 
the  square-threaded  screw 
constitute  a  narrow  inclined 
plane,  but  wrapped  around 
a  cylinder  instead  of  being  flat.  If  you  turn  such  a  screw 
with  your  pencil-point  in  the  channel  between  the  threads, 
the  point  will  rise  gradually,  just  as  it  would  rise  along  an 
inclined  plane. 

Most  screws  are  made  with  a  V-thread,  as  at  P  (Fig.  64), 
instead  of  the  square  one ;  but  you  will  easily  see  that  this 
in  no  way  changes  the  principle  of  their  action. 

The  Nut  is  a  piece  of  metal  bored  out  and  then  cut 
with  a  spiral  channel  in  such  a  way  as  just  to  fit  the  screw 
(see  N,  Fig.  64).  When  a 
screw  is  driven  into  wood,  ^ — 
the  fibers  of  the  wood  are 
crushed  into  such  a  form  as 
fit  the  threads  of  the  screw 
just  as  the  nut  does  at  N. 

One  application  of  the  screw 
as  a  machine  is  to  produce  great 
pressures.  Suppose  the  nut  N 
(Fig.  64)  to  be  held  firmly  in  place 
and  the  handle  A  of  a  lever  in  the  head  of  the  screw  to  be  turned  in  such 
away  as  to  advance  the  screw.  Any  object  at  C  would  be  pushed  upon 
with  a  great  pressure,  Or  the  screw  may  be  held  from  advancing,  and 
the  nut  will  then  be  pressed  forward  or  backward. 

The  Pitch  of  the  Screw  is  the  distance  between  the 
successive  threads,  as  G'  H'  or  H'  I',  etc.  (Fig.  63).  For  in- 


FIG.  64.— SCREW  AND  NUT. 


LAW  OF  THE  SCREW.  159 

stance,  if  this  distance  were  -fa  inch,  the  screw  would  be 
said  to  have  a  "  pitch  "  of  -fa  of  an  inch ;  or  it  would  be 
said  that  the  screw  had  20  threads  to  the  inch.  From  the 
law  of  the  inclined  plane,  it  will  be  seen  that  the  pitch  of 
the  screw  corresponds  to  the  height  of  the  plane  and  the 
circumference  to  the  base.  The  law  of  the  screw  could 
then  be  deduced  from  that  of  the  inclined  plane,  but  it  is 
better  to  deduce  it  directly. 

Suppose  the  screw  turned  by  energy  causing  a  force  P  at  A  always 
at  right  angles  to  the  lever  A  D.  Let  A  B  be  the  arm  of  this  force ; 
then  the  distance  S  passed  over  by  A  in  one  turn  of  the  screw  will  be 
the  circumference  of  a  circle  with  A  B  as  a  radius  (viz.,  S  =  2  x  3-141 
X  A  B).  The  work  done  upon  the  machine  will  be  P  x  S.  In  one 
turn  the  screw  will  be  advanced  at  C  by  a  distance  equal  to  its  pitch, 
which  we  will  call  s.  Let  F  represent  the  force  exerted  by  C.  The 
work  done  at  C  will  then  be  F  x  s.  Neglecting  friction,  then,  we  must 

c 
have  F  x  s  =  P  x  S,  or  F :  P  =  S  :  s ;  orF  =  P-. 

6 

By  way  of  example,  if  we  had  a  screw  of  a  pitch  of  £  inch  turned 
by  a  force  of  50  pounds  at  the  end  of  a  lever  of  length  A  B  =  2  feet, 
how  much  work  could  that  screw  perform 
per  rotation  and  how  much  force  or  pressure 
could  it  produce  at  C  ?    The  work  it  could 


FIG.  65.— JACK-SCREW.  FIG.  66.— LETTER-COPYING  PRESS. 

do  per  rotation  would  be  F  x  s  =  P  x  S.    Now,  S  =  2  x  3'14  x  2  =  12-56 
feet  and  P  =  50  pounds,  .  • .  work  =  50  x  12-56  =  628  foot-pounds. 

g 
The  force  or  pressure  F  which  it  could  produce  would  be  F  =  P  — . 


160 


MACHINES. 


FIG.  67.— THE  ENDLESS  SCREW. 


Now  8  must  be  expressed  in  feet  if  S  is.    Then  s  =  £  inch  =  £  x  ^ 

fi28 
=  sV  feet    /.  F  =  — —  =  628  x  60  =  37,680  pounds  =  18-84  tons. 

¥o 

A  screw  of  about  these  dimensions,  called  a  Jack-Screw  (Fig.  65), 
is  used  in  raising  buildings  temporarily  from  their  foundations,  as  well 
as  for  other  purposes  where  great  force  is  necessary.  The  common 
letter-copying  press  (Fig.  66)  is  another  example  of  the  application  of 
the  screw. 

Endless  Screw. — Besides  its  application  in  machines  for 

producing  great  press- 
ures and  lifting  heavy 
masses,  the  screw  is  used 
in  various  ways  for  trans- 
mitting motion.  The 
endless  screw  (Fig.  67) 
illustrates  this.  When  it 
rotates,  its  threads  turn 
the  toothed  wheel.  A 

rapid  speed  of  the  shaft  of  the  screw  is  changed  into  a  slow 

motion  of  the  wheel. 

The  Pulley  is  merely  a  wheel,  usually  grooved  on  its 
face  to  hold  a  cord  or  rope,  and  suitably  mounted  on  an 
axle.  It  serves  merely  to  change  the  direction  of  the  pull 
of  the  rope  passing  over  it.  For  in- 
stance, the  pulley  P  (Fig.  68)  changes 
the  direction  of  the  pull  A  exerted 
by  the  hand  to  the  desired  direction, 
B.  If  friction  be  neglected,  the  force 
B  equals  the  force  A.  The  relative 
and  absolute  directions  of  the  parts 
A  and  B  of  the  rope  make  no  differ- 
ence whatever.  Take  the  familiar 
case  of  two  bodies  of  weights  W,  and 
Wa  hanging  on  a  cord  laid  over  a  pulley  (P,  Fig.  12) :  you 
know  that,  except  for  friction  and  weight  of  cord,  W,  must 


FIG.  68.— THE  PULLEY. 


PULLEYS. 


161 


equal  Wa  in  order  to  balance.     This  is  only  a  special  case 
of  the  pulley  where  the  forces  happen  to  be  vertical. 

If  you  pull  steadily  upon  the  end  of  any  rope  or  cord  in  any  po- 
sition, there  must  be  at  every  point  throughout  the  cord  a  pull  of  the 
same  amount,  except  for  slight  differences  due  to  the  weight  of  the 
cord  itself  or  to  friction. 

A  mechanical  advantage  may  be  gained  by  combining 
two  or  more  pulleys.  In  Fig.  69,  A  is  a  fixed  and  B  a  free 
pulley.  The  rope 
is  fastened  to  the 
bottom  of  the 
block  A,  thence 
goes  under  B, 
then  over  A,  and 
then  passes  to 
any  point  P  at 
which  the  power 
is  applied.  The 
load  L  to  be 
lifted  is  hung 
upon  B.  Note 
that  there  are  two  lines  of  rope  connecting  A  and  B.  If, 
now,  P  is  pulled  sufficiently  to  lift  L,  you  will  see  that  for 
every  foot  that  B  (and  therefore  L)  is  raised,  each  line  of 
rope  between  A  and  B  must  be  shortened  one  foot,  and 
therefore  two  feet  of  rope  must  be  taken  over  A  toward  P. 
That  is,  for  each  foot  that  L  is  lifted,  P  must  move  back 
through  two  feet. 

In  the  second  set  of  pulleys,  the  pulleys  C  and  D  are 
fixed  and  E  is  free.  There  are  three  lines  of  rope  connect- 
ing the  fixed  and  free  pulleys.  Then  for  each  foot  that  L 
rises,  three  feet  of  rope  must  be  pulled  back  toward  P.  In 
the  third  set,  there  are  four  lines  of  rope  between  the  fixed 
and  free  pulleys.  Hence  P  moves  back  four  feet  for  each 
foot  of  rise  of  L. 


FIG.  69. — COMBINATIONS  OP  FIXED  AND  FREE  PULLEYS. 


162  MACHINES. 

Law  of  the  Pulley. — In  every  case,  then,  the  law  of 
the  pulley  is  as  follows :  Let  S  represent  the  distance  through 
which  the  moving  force  P  is  exerted,  and  s  that  through 
which  the  load  L  is  raised.  The  work  done  by  P  will,  be 
P  S,  and  this  must  be  equal,  neglecting  friction,  to  the  work 
L  s  done  upon  the  load.  Then  P  S  =  L  s,  or  P  :  L  =  s  :  S, 

orL  =  P-. 

s 

In  all  cases  S  :  s  =  w  :  1,  where  n  is  the  number  of  lines 
connecting  the  fixed  and  movable  pulleys. 

EXAMPLE. — If  we  wish  to  raise  a  load  L  of  1,000  pounds  by  the 
third  set  of  pulleys,  how  much  would  be  the  least  pull  required  at  P I 
In  this  set  n  =  4  .-.  P  :  1,000  =  1:4,  therefore  P  =  J-«p  =  250  pounds. 

Note  that  in  this  as  in  other  machines  the  working  force  must  be 
greater  by  an  amount  necessary  to  do  the  work  of  friction  and  of  ac- 
celeration. The  amount  of  friction  in  the  pulleys  is  so  great  that  a 
very  large  part  of  the  work  is  wasted,  and  there  is  no  practical  gain  in 
using  a  pulley  of  more  than  two  or  three  sheaves.  The  mechanical  ad- 
vantage gained  ds  an  increase  of  force. 

For  the  sake  of  compactness,  where  there  are  several  pulleys  at 
each  end  they  are  put  side  by  side  in  a  "  block,"  as  shown  in  the  fourth 
set  in  Fig.  69.  The  single  wheels  in  such  a  block  are  called  the 
"  sheaves."  The  whole  system  is  sometimes  called  a  "  tackle." 

The  Knee  or  Toggle  Joint. — Two  bars  jointed  at  A 
and  pressing  at  B  and  C  against  any  two  desired  objects, 


p 

FIG.  70.— THE  KNEE  OR  TOGGLE  JOINT. 

form  this  machine.  The  bars  A  C  and  A  B  are  almost  in 
line,  so  that  the  angle  B  A  0  is  nearly  180  degrees.  If  a 
force  is  applied  at  the  joint,  as  shown  in  amount  and  direc- 
tion by  P,  it  will  produce  large  forces  Fj  and  F2  tending  to 
push  the  surfaces  at  B  and  C  apart.  It  will  be  seen  that  the 


THE  EQUAL-AKM  BALANCE. 


163 


nearer  in  line  A  B  and  A  0  come,  the  greater  the  forces  F! 
and  Fo  produced  by  a  given  working  force  P. 

The  Equal- Arm  Balance  is  an  adaptation  of  the  lever 
for  the  purpose  of  weighing.  It  consists  of  the  "  beam  " 
A  B  (Fig.  71),  supported  on  the  knife-edge  C,  usually  a 
three-cornered  steel  bar  passing  horizontally  through  the 
beam  at  right  angles  to  it.  The  sharp  lower  edge  of  C  rests 
on  steel  or  agate  supporting  plates,  D.  At  the  ends  F  and 
G  of  the  beam  are  two  smaller  knife-edges  parallel  to  the 
other,  but  edge  upward.  These  edges  are  at  equal  distances 


FIG.  71.— THE  EQUAL- ARM  BALANCE. 


from  the  central  knife-edge,  and  on  this  the  accuracy  of  the 
balance  depends.  Hung  upon  these  end  knife-edges  by 
means  of  steel  or  agate  plates  are  the  scale-pans  H  and  I. 
In  one  pan  is  placed  the  object  to  be  "  weighed,"  and  in  the 
other  are  placed  the  standard  masses.  A  pointer  P  is  at- 
tached to  the  beam  at  0,  and  as  the  beam  tips,  this  moves 
'over  a  graduated  scale. 

The  equal-arm  balance  has  been  carried  to  a  very  high  grade  of 
accuracy.  It  has  been  made  so  sensitive  as  to  detect  a  difference  of 
much  less  than  one  millionth  part  of  the  whole  mass  upon  it,  and  to 
show  the  weight  of  less  than  y^  milligramme.  The  balance  used  in 


164  'MACHINES. 

ordinary  chemical  analysis  will  weigh  to  about  1  part  in  100,000,  and 
will  measure  O'l  milligramme  in  masses  of  a  few  grammes. 

Weighing*. — The  use  of  the  balance  is  called  Weighing. 
It  is  a  process  for  ascertaining  the  mass  of  any  body,  and  de- 
pends on  the  principle  of  the  equilibrium  of  moments.  The 
arm  of  one  force  is  0  F,  that  of  the  other  C  G,  and  these  are 
made  exactly  equal,  as  are  also  the  weights  of  the  pans.  The 
balance  can  swing  evenly  only  when  equal  forces  are  applied 
at  F  and  G — that  is,  when  the  weights  of  the  substances  in 
the  pans  are  equal. 

The  process  is  as  follows :  The  balance  is  set  swinging  without  a 
load,  to  see  if  it  is  in  "  adjustment " — i.  e.,  if  it  swings  equally  on  each 
side  of  the  middle  point ;  if  not,  it  is  adjusted  until  it  does  so.  The 
body  whose  mass  is  to  be  determined  is  then  put  into  one  pan,  usually 
the  left-hand  one  for  convenience.  Masses  from  the  graded  set  of 
masses  (pages  81  and  89)  are  put  into  the  other  pan  until  the  pointer 
again  swings  equally.  The  weight  of  the  unknown  body  and  of  the 
known  masses  in  the  pan  are  thus  shown  to  be  equal ;  therefore,  the 
masses  are  also  equal.  The  mass  of  the  unknown  body  is  found  by 
adding  the  known  masses  used. 

If  the  balance  arms  C  F  and  C  Gr  are  not  exactly  equal,  then  there 
will  be  an  error  in  the  result.  This  may  be  avoided  by  putting  the  ob- 
ject in  the  right-hand  pan,  and  filling  shot  or  sand  into  the  left  until 
equilibrium  is  obtained ;  then  removing  the  object  and  putting  in 
standard  masses  until  equilibrium  is  again  obtained.  A  rough  balance 
may  thus  be  made  to  give  much  better  results. 

QUESTIONS. — Show  how  the  Screw  is  a  modification  of  the  inclined  plane.  De- 
scribe the  Nut.  Define  the  pitch  of  a  screw.  How  may  the  screw  be  used  to 
obtain  great  pressure  ?  State  the  law  of  the  screw  as  thus  used. 

A  jack-screw,  with  a  pitch  of  one  quarter  of  an  inch,  is  turned  with  a  force  of  75 
pounds  at  the  end  of  a  lever  of  2  feet ;  how  much  pressure  could  the  screw 
produce,  neglecting  friction  ?  How  much  work  can  it  do  per  turn  ? 

Describe  the  Endless  Screw.  "What  is  a  Pulley  ?  What  is  its  use  ?  How  can  a 
mechanical  advantage  be  gained  by  the  use  of  a  combination  of  pulleys  ? 
State  the  law  of  the  pulley.  Show  how  this  is  true  from  the  amount  of  rope 
drawn  through  each  of  the  pulleys.  State  the  rule  for  finding  the  ratio  of 
motion  of  power  to  load.  In  each  of  the  four  sets  of  pulleys  of  Fig.  69,  what 
load  would  a  power  of  100  pounds  just  balance  ?  Describe  the  Knee  or  Toggle 
Joint.  In  Fig.  70,  suppose  that  P  =  100  pounds,  what  would  be  the  amount  of 
F,  ?  What  would  be  the  force  with  which  D  and  E  would  be  pressed  upon  ? 
Describe  the  balance  ;  the  process  of  weighing. 


MISCELLANEOUS  QUESTIONS.  165 


MISCELLANEOUS   QUESTIONS  AND  PROBLEMS. 

Suggest  a  reason  why  rollers  are  used  in  moving  heavy  blocks  of  granite. 

When  brakes  are  applied  to  the  wheels  of  a  heavily-loaded  stage-coach  hi  de- 
scending a  hill,  what  is  accomplished,  and  why  ?  , 

Why  is  it  more  difficult  for  a  pair  of  horses  to  start  a  street-car  than  to  keep  it  in 
motion  after  it  is  started  ? 

Explain  the  reason  why  you  can  go  so  fast  on  skates.  Why  sleighs  are  used  in 
winter  instead  of  wagons. 

Do  you  find  it  easier  to  walk  on  a  carpeted  floor  than  one  of  polished  hard  wood  ? 
Think  of  a  reason. 

Could  a  carriage  progress  without  friction  ?  Can  a  train  be  moved  if  the  rails 
are  thoroughly  lubricated  ?  Grasshoppers  crushed  by  the  wheels  of  the  cars 
have  been  the  means  of  stopping  trains  in  the  West. 

Analyze  the  action  of  a  tack-hammer  in  drawing  a  nail.  Where  is  the  fulcrum  ? 
The  weight  ?  The  power  ? 

Of  what  order  of  lever  is  the  common  chopping-kuife  ?  A  pair  of  tongs  ?  A 
nut-cracker  ?  A  piano-pedal  ? 

The  farther  from  the  rowlocks  you  grasp  the  oars,  the  more  easily  you  propel 
your  boat.  Why  ?  What  do  we  here  mean  by  "  more  easily  "  ? 

Did  you  ever  attempt  to  lift  a  ladder  from  the  ground  by  walking  under  it  and 
grasping  round  after  round  in  succession  ?  Why  did  you  experience  difficulty, 
or  were  perhaps  forced  to  give  up  the  feat,  as  you  approached  the  bottom  ? 

Account  for  the  difficulty  of  holding  out  a  heavy  weight  at  arm's  length. 

A  machine  takes  up  4  foot-pounds  of  energy  for  every  2  foot-pounds  it  gives  out ; 
what  is  its  efficiency  ? 

A.  dynamo-electric  machine,  having  an  efficiency  of  93  per  cent,  receives  2,000 
foot-pounds  of  energy  ;  how  much  electrical  energy  does  it  give  out  ?  It  re- 
ceives energy  at  the  rate  of  40  horse-power ;  at  what  rate  does  it  give  out 
electrical  energy  ? 

With  a  pair  of  tongs  3  feet  long  a  pressure  of  5  pounds  is  desired  between  the 
points  ;  the  hands  are  held  one  foot  from  the  hinge  ;  how  much  force  must 
be  exerted  ? 

In  Fig.  54  find  the  leverage  by  measurement.  If  the  barrel  weighs  150  pounds, 
how  much  pressure  must  be  exerted  ?  What  gain  of  work  is  made  ? 

Does  a  horse  drawing  a  carriage  up-hill  where  there  is  a  rise  of  1  in  20  really  lift 
one  twentieth  of  the  load  ?  Explain  why. 

Why  does  the  driver  of  a  heavy  load  in  ascending  a  hill  take  a  zigzag  course  ? 

A  farmer,  in  forcing  a  stump  from  the  ground,  uses  a  crow-bar  6  feet  long,  which 
he  rests  on  a  stone  5  feet  from  the  end  where  his  hand  is  applied.  The  resist- 
ance of  the  stump  is  equal  to  a  weight  of  500  pounds ;  how  great  a  pressure 
must  he  exert  to  move  it  ? 

A  man  weighing  180  pounds  and  a  boy  of  60  pounds  are  teetering  on  i.  .board  12 
feet  long.  That  they  may  balance  each  other,  how  near  must  the  man  t^t  to 
the  horse  on  which  the  board  rests  ? 

Four  men  are  drawing  in,  with  a  capstan,  an  anchor  that  weighs  1,000  pounds. 
The  barrel  of  the  capstan  has  a  radius  of  6  inches.  The  circle  described  by  the 
handspikes  has  a  radius  of  5  feet.  How  great  a  pressure  must  each  of  the  four 
men  exert  to  move  the  anchor  ? 

With  a  fixed  pulley,  how  great  a  power  will  it  take  to  hoist  a  weight  of  50  pounds, 
20  per  cent,  or  one  fifth,  being  added  for  friction  ? 


1QQ  THE  THREE  STATES  OF  MATTER. 

A  book-binder  has  a  press,  with  a  screw  whose  threads  are  one  third  of  an  inch 
apart,  and  a  nut  worked  by  a  lever  which  describes  a  circle  of  8  feet ;  how 
great  a  pressure  will  a  power  of  5  pounds  applied  at  the  end  of  the  lever  pro- 
duce, the  loss  by  friction  being  equivalent  to  240  pounds  ? 


THE  THREE  STATES  OF  MATTER.— 
SOLIDS. 

DIFFERENCES  IN  THE  THREE  STATES  OF  MATTER. 

Matter  exists  in  Three  Conditions  or  states,  which 
are  called  respectively  the  Solid,  the  Liquid,  and  the  Gaseous 
State.  Liquids  and  gases  are  also  called  Fluids. 

Solids. — You  are  familiar  with  matter  in  what  is  called 
the  solid  state.  A  stone,  a  piece  of  wood,  metal,  or  ice,  are 
every-day  examples  of  solids.  If  you  think  about  all  the 
solid  substances  which  you  can  call  to  mind,  you  will  see 
that  they  have  this  property  in  common,  viz. :  They  retain 
their  shape  when  left  to  themselves,  and  can  only  be  made  to 
change  shape  by  the  application  of  energy. 

Liquids,  on  the  other  hand  (water  and  mercury  are  every- 
day types),  must  be  held  in  a  vessel  of  some  kind.  If  left  to 
themselves  they  do  not  retain  their  form,  but  spread  out  over 
the  surface  on  which  they  are  placed.  Owing  to  the  action 
of  their  weight,  liquids  do  not  require  to  be  held  down  at 
their  upper  surface,  but  can  be  kept  (except  for  evapora- 
tion) in  a  vessel  open  at  the  top.  All  liquids  may  probably 
be  red  Toed  to  solids  by  sufficiently  great  cooling.  Nearly 
all  have  been  thus  solidified. 

Gases,  like  liquids,  require  to  be  held  in  a  retaining 
vessel ;  but,  unlike  liquids,  if  left  to  themselves,  gases  will 
spread  or  expand  in  all  directions.  Hence  the  vessel  con- 
taining them  must  be  closed  on  all  sides.  Air  is  a  common 


SOLIDS.  167 

example  of  a  gas,  or  rather  of  a  mixture  of  gases.  All  gases 
may  be  reduced  to  liquids :  some  by  great  compression 
alone;  others  by  great  cooling  alone;  others  require  both 
cooling  and  compression  combined. 

The  Molecular  Differences  in  the  Three  States 

are  as  follows :  In  all  three  states  the  molecules  are  in  the 
continual  to-and-fro  motion  of  heat-energy,  but  with  this 
difference — in  the  solid  state,  the  molecule  does  not  wander 
about  through  the  body,  but  remains  always  at  or  very  near 
the  same  point,  simply  moving  to  and  fro,  somewhat  as  a 
pendulum-bob  vibrates  about  its  point  of  rest,  but  more 
irregularly.  In  the  liquid  state,  every  molecule  does  wander 
in  a  very  irregular  path,  and  somewhat  slowly,  through  the 
body  of  the  liquid,  being  now  at  one  point  and  presently  at 
another,  jostling  violently  around  among  its  neighbors.  In 
gases,  each  molecule  moves  around  as  in  liquids,  but  much 
faster  and  with  a  freer  motion.  The  spaces  between  the 
molecules  are  much  greater,  so  that  they  can  move  farther 
without  jostling  against  one  another. 

We  have  now  to  consider  some  of  the  properties  and 
laws  of  matter  in  these  three  states. 

PROPERTIES  OF  SOLIDS. 

Cohesion.  —  Adhesion.  —  Take  hold  of  the  ends  of 
your  pencil  with  your  fingers,  and  pull  lengthwise  (not 
crosswise),  as  if  trying  to  pull  it  apart.  It  resists  so  strongly 
that  you  can  not  do  so.  Try  to  break  any  object  in  any 
way ;  the  breaking  is  more  or  less  resisted.  Break  a  small 
stick  of  wood  by  pulling  or  bending.  It  breaks  by  the 
pulling  apart  of  its  molecules.  Put  the  broken  surfaces 
again  together,  and  they  do  not  hold.  Yet  the  only  differ- 
ence in  conditions  is  that  you  are  unable  to  get  them  back 
to  the  same  closeness  of  contact  that  they  had  before. 

There  appears,  then,  to  be  some  form  of  energy  which 
causes  an  attractive  force  between  molecules  of  the  same 


1()8  SOLIDS. 

kind,  this  force  being  very  great  at  extremely  short  dis- 
tances, but  being  so  slight  as  to  be  imperceptible  at  dis- 
tances of  a  few  thousandths  of  an  inch.  The  property  of 
possessing  this  force  is  called  Cohesion,  and  the  force  is 
called  the  Force  of  Cohesion,  or  often  merely  Cohesion. 

A  similar  force  exists  between  surfaces  of  matter  of 
different  kinds.  It  is  shown  when  you  try  to  pull  apart 
pieces  of  wood  glued  together,  or  cemented  bricks.  The 
force  which  holds  the  glue  to  the  wood  or  the  cement  to 
the  brick  is  an  attraction  between  materials  of  different 
kinds,  and  is  called  Adhesion.  The  distinction  between 
cohesion  and  adhesion  is  of  little  consequence ;  they  are 
probably  both  due  to  the  same  form  of  energy. 

Cohesion  and  adhesion  exist  in  liquids,  and  probably  in 
gases  to  a  very  limited  extent. 

It  is  to  cohesion  that  the  strength  or  tenacity  of  materials  is  due, 
and  the  limit  of  strength  is  reached  when  the  force  applied  to  the 
body  is  equal  to  the  cohesive  force  exerted  by  the  body  in  opposition 
to  that  force.  That  surfaces  may  be  brought  so  closely  into  contact  as 
to  cohere  or  adhere,  is  shown  by  the  fact  that  gluing,  cementing, 
soldering,  welding,  varnishing,  etc.,  are  possible. 

EXPERIMENT. — Cut  a  lead  bullet  in  two,  and  make  the  fresh 
surfaces  exceedingly  smooth  and  flat.  Press  them  firmly  together. 
They  will  cohere  perceptibly.  Lay  a  very  smooth  piece  of  plate-glass 
on  the  table.  Place  upon  it  another  (of  a  little  larger  size,  for  con- 
venience of  lifting  by  the  edges),  and  put  a  weight  upon  them.  After 
a  while  carefully  remove  the  weight,  and  pick  up  the  top  plate.  The 
lower  plate  will  be  found  to  cohere  more  or  less  strongly.  Two  such 
plates  left  lying  together  for  months  or  years  may  cohere  so  strongly 
as  to  be  more  easily  broken  than  pulled  apart.  Machinists  and  others 
who  have  occasion  to  make  very  truly  plane  surfaces  have  what  they 
call  "surface  plates,"  by  which  to  test  the  surfaces  which  they  are 
making.  These  consist  usually  of  three  steel  plates  which  have  been 
alternately  ground  together  in  pairs  until  each  fits  both  the  others, 
and  all  are  therefore  plane.  If  these  be  cleaned  and  put  together, 
they  adhere  quite  firmly,  even  in  vacuo. 

Welding  is  a  process  of  making  metals  cohere  or  ad- 
here. The  surfaces  to  be  joined  are  cleaned  and  made  of 


HARDNESS.— DUCTILITY.— MALLEABILITY.         169 

suitable  shape.  They  are  then  heated,  and  while  hot  are 
cleaned  again  by  means  of  a  material  called  a  flux  (rosin, 
borax,  etc.),  and  brought  into  contact.  They  are  then 
hammered  or  pressed  together  to  bring  them  into  closer 
contact,  and  allowed  to  cool.  When  cold,  they  cohere  or 
adhere  nearly  or  quite  as  strongly  as  the  other  parts  of  the 
material.  The  blacksmith  can  thus  weld  wrought-iron 
easily  and  a  few  other  metals  with  difficulty ;  but  the  pro- 
cess of  welding  by  electricity  has  rendered  this  property 
available  in  the  case  of  almost  all  metals. 

Hardness. — A  body  is  said  to  be  harder  than  another 
when  it  is  capable  of  scratching  the  former  but  not  of  being 
scratched  by  it.  The  diamond  is  the  hardest  of  all  solids. 
Hardness  is  made  use  of  in  mineralogy  as  a  means  of  identi- 
fying minerals.  By  sudden  cooling  from  a  high  tempera- 
ture, steel  and  some  other  bodies  acquire  great  hardness, 
usually  accompanied  with  increased  brittleness.  Bodies 
thus  treated  are  said  to  be  tempered. 

Ductility  is  that  property  which  renders  some  materials 
capable  of  being  drawn  out  into  wires  or  threads.  Glass 
when  hot  can  be  spun  into  threads.  Warm  wax  can  also 
be  thus  treated.  Many  metals  when  cold  possess  the  same 
property.  Thus,  gold,  silver,  platinum,  iron,  copper,  palla- 
dium, aluminum,  zinc,  tin,  lead,  can  all  be  drawn  into  wires 
when  cold  by  pulling  them  through  hard  metal  plates  bored 
with  holes  of  suitable  sizes.  Gold  is  the  most  ductile  metal, 
and  the  others  stand  in  the  list  above  in  the  order  of  their 
ductility. 

Malleability  is  that  property  which  renders  a  body 
capable  of  being  hammered  or  rolled  into  sheets.  Gold, 
copper,  and  other  metals  are  quite  malleable.  This  prop- 
erty and  ductility  are  closely  related ;  but  the  metals 
do  not  stand  in  precisely  the  same  relative  order  for  the 
two.  Consult  pages  62  and  67. 
12 


170  SOLIDS. 

Elasticity. — From  the  experiments  described  on  pages 
49  to  52,  you  have  learned  that  when  a  force  is  applied  to  a 
body  which  is  prevented  from  being  accelerated,  the  body  is 
changed  in  size  or  form ;  also,  that  when  the  applied  force  is 
removed,  the  body  will  more  or  less  completely  regain  its 
original  form.  The  force  acting  in  such  a  case  is  called  the 
Stress ;  the  change  in  form  produced  during  its  action  is 
the  Strain.  Elasticity  is  that  property  by  virtue  of  which 
a  body  (whether  solid,  liquid,  or  gaseous)  requires  force  to 
change  its  bulk  or  shape,  and  resumes  its  form  when  the 
force  is  removed. 

Suppose  you  were  to  take  a  round  rod  of  rubber  a  foot  long  and  an 
inch  in  diameter  and  a  piece  of  steel  of  the  same  size,  and  were  by  any 
means  to  hold  each  stretched  by  the  one-thousandth  part  of  its  length. 
To  do  so  would  obviously  require  a  much  greater  force  with  the  steel 
than  with  the  rubber.  Which  is  the  more  elastic  ?  You  would  per- 
haps naturally  say  the  rubber ;  but  this  is  not  the  case.  The  rubber 
is  the  more  extensible,  but  the  steel  is  the  more  highly  elastic.  The 
elasticity  of  a  body  is  measured  by  the  amount  of  force  required  to 
produce  a  specified  change  of  size  or  form ;  hence  the  greater  the  force 
required,  the  greater  the  elasticity. 

When  we  are  dealing  with  the  reduction  of  the  volume 
or  length  of  a  body  by  pressure,  we  speak  of  compression  ; 
when  with  the  increase  of  length,  of  extension  ;  when  with 
its  bending,  of  flexibility.  The  latter  is,  as  stated  on  page 
51,  a  combination  of  compression  and  extension.  If  we  say 
that  one  body  is  twice  as  compressible  or  extensible  or  flexi- 
ble as  another,  we  mean  that  equal  forces  will  produce  twice 
the  amount  of  compression  or  extension  or  bending  on  pieces 
of  the  same  size.  In  such  a  case,  the  first  body  would  be 
only  half  as  elastic  as  the  second. 

Some  substances  can  be  stretched,  compressed,  or  bent 
but  a  little  before  breaking,  and  are  said  to  be  brittle.  Sub- 
stances the  reverse  of  these  are  called  tough. 

Most  substances  when  strained  do  not  entirely  recover 
their  original  forms.  They  are  therefore  said  to  be  imper- 


ELASTICITY.— STRUCTURE.  171 

fectly  elastic,  while  those  which  do  recover  completely  are 
called  perfectly  elastic.  Many  substances  appear  to  be  per- 
fectly elastic  if  not  strained  beyond  a  certain  amount. 

Hold  in  the  hand  or  under  a  clamp  one  end  of  a  bit  of  iron  or  cop- 
per wire.  Pull  the  other  end  aside  a  very  little  so  as  to  produce  slight 
bending,  and  let  it  go.  After  vibrating  for  a  while  it  will  settle  down 
in  its  original  position  of  rest.  So  far  as  you  can  see,  it  is  perfectly 
elastic.  Repeat  the  experiment,  bending  the  wire  a  little  more  each 
time.  You  will  soon  find  that  the  recovery  is  not  perfect,  but  that  the 
wire  has  been  "  bent,"  or  has  taken  what  is  called  a  "  permanent  set." 
Its  elasticity  is  perfect  only  below  a  certain  amount  of  strain. 

This  amount  or  limit  below  which  the  substance  is  perfectly  elas- 
tic, or  sensibly  so,  is  called  the  limit  of  elasticity.  Some  solids  (steel, 
glass,  etc.)  can  be  strained  nearly  to  the  breaking  point  without  pass- 
ing this  limit ;  others  (wax,  rubber,  copper,  gold,  and  ductile  materials 
generally)  reach  the  limit  at  much  less  strain  than  is  required  to  break 
them.  If  a  substance  is  kept  in  a  strained  condition  for  a  long  time, 
it  will  generally  show  a  permanent  set  on  being  released,  even  when  it 
has  been  strained  much  less  than  up  to  what  appears  to  be  its  limit  of 
elasticity  for  strains  of  short  duration. 

Structure. — Examine  and  compare  a  lump  of  blue 
vitriol  (copper  sulphate),  a  piece  of  mica,  a  bit  of  pine 
wood,  a  piece  of  sandstone,  a  fragment  of  glass.  You  will 
find  the  lump  of  vitriol  made  up  of  a  number  of  more  or 
less  regularly  shaped  masses  of  the  salt.  It  is  composed  of 
imperfect  crystals,  and  is  said  to  have  a  crystalline  struct- 
ure. All  crystals  split  or  "  cleave  "  more  readily  in  some 
directions  than  in  others.  Thus  mica  splits  into  thin  plates 
or  layers  (lam'-ince),  and  is  therefore  said  to  have  a  laminated 
structure.  Wood  splits  easily  along  the  grain  or  fiber,  and 
is  said  to  have  a  fibrous  structure.  Sandstone  is  made  up 
of  a  multitude  of  grains,  and  is  therefore  described  as  having 
a  granular  structure.  Glass  splits  equally  well  in  all  direc- 
tions, and  appears  to  be  without  structure,  which  is  expressed 
by  saying  that  it  has  an  amorphous  (without  form)  structure. 

EXPERIMENT. — Dissolve  a  small  handful  of  alum  in  about  twice  its 
weight  of  hot  water.  Hang  a  thread  down  into  the  middle  of  the 


172  SOLIDS. 

liquid  and  stand  it  aside  in  a  quiet  place  free  from  dust.  In  a  few 
hours  or  days  there  will  be  found  on  the  thread  crystals  of  alum  more 
or  less  perfect.  Similar  experiments  may  be  made  with  copper  sul- 
phate, common  salt,  and  other  substances. 

If  in  the  winter  you  catch  snow-flakes  on  a  dark  cloth,  you  will  see, 
especially  well  with  a  magnifier,  that  they  are  usually  composed  of 
regular  and  beautiful  crystals  of  ice  (see  page  277).  The  frost  which 
forms  on  the  window-pane  is  also  generally  crystalline. 

Viscosity. — Certain  substances  which  we  commonly  re- 
gard as  solids  do  not  strictly  fulfill  the  definition  of  a  solid 
as  a  substance  which  holds  its  form  when  left  to  itself. 

EXPERIMENT. — Fasten  one  end  of  a  stick  of  sealing-wax  so  that  it 
projects  horizontally,  as  the  stick  in  Fig.  14.  Leave  it  for  a  day  or 
two.  The  projecting  end  will  have  become  permanently  bent  down- 
ward. A  piece  of  pitch  left  lying  upon  a  table  will  after  several  days 
be  found  to  have  flowed  out  into  a  flat  mass,  as  thick  molasses  would 
have  done  much  more  quickly. 

This  slow  change  of  form  is  due  to  a  sort  of  flowing  of 
the  parts  of  the  substance.  Solids  acting  in  this  way  under 
ordinary  conditions  may  properly  be  considered  as  imper- 
fectly solid.  They  are  said  to  be  viscous. 

QUESTIONS.— What  are  the  three  states  of  matter  ?  What  is  the  characteristic  by 
which  we  recognize  Solids  ?  Give  examples  of  solids.  Is  putty  a  solid  ?  Is  ice 
a  solid  ?  What  is  the  main  distinction  between  solids  and  liquids  ?  Give  exam- 
ples of  liquids.  Are  sealing-wax  and  pitch  liquids  ?  How  may  liquids  be  ren- 
dered solid  ?  What  is  the  chief  distinction  between  gases  and  liquids  ?  Give 
examples  of  gases.  How  may  gases  be  reduced  to  the  liquid  condition  ?  Give 
an  example  of  some  substance  which  you  know  of  as  capable  of  existing  in 
all  three  states.  State  the  molecular  differences  between  the  three  states. 

Show  that  Cohesion  and  Adhesion  exist  in  solids.  What  is  the  distinction  be- 
tween the  two  terms  ?  Do  these  properties  exist  in  liquids  and  gases  ?  To  what 
extent  ?  Is  cohesion  or  adhesion  perceptible  at  long  distances  ?  Give  examples 
to  show  what  the  distance  is  at  which  they  are  perceptible.  To  what  is  the 
strength  or  tenacity  of  materials  due  ?  To  what  form  of  energy  is  cohesion 
due  ?  On  what  does  the  possibility  of  welding,  soldering,  gluing,  etc.,  depend  ? 
Describe  these  processes.  Describe  an  experiment  showing  the  adhesion  of 
liquids  to  solids.  One  showing  the  cohesion  of  liquids.  What  is  meant  by 
Hardness  ?  By  Temper  ?  By  Ductility  ?  Give  examples. 

Define  Malleability,  Elasticity,  Stress,  Strain.  Which  is  the  more  elastic,  iron  or 
wood  ?  Brass  or  rubber  ?  WThich  is  more  easily  extensible  ?  What  is  meant 
by  Brittleness  ?  By  Toughness  ?  Illustrate.  Give  examples  of  permanent  set. 
What  is  meant  by  limit  of  elasticity  ?  Describe  crystalline,  laminated,  fibrous, 
granular,  and  amorphous  structure.  Define  Viscosity  ;  give  an  example. 


LIQUIDS  AND  GASES. 

PROPERTIES  OF  LIQUIDS. 

Cohesion. — Adhesion. — If  you  dip  a  pencil  or  your 
finger  into  water,  you  will  find,  on  drawing  it  out,  that  some 
water  clings  to  it.  This  is  because  the  water  adheres  to  the 
pencil  or  finger,  and  also  coheres — that  is,  holds  together. 
Most  other  liquids  act  similarly ;  but  mercury  and  certain 
molten  materials  do  not,  although  they  possess  the  proper- 
ties of  cohesion  and  adhesion. 

NOTE.— The  properties  of  liquids  and  gases  discussed  in  the  following  sections 
may  be  illustrated  measurably  with  the  apparatus  shown  above.  Methods  of 
constructing  simply  and  cheaply  various  essential  pieces  are  suggested  in  the 
text.  No.  1  represents  an  adhesion  plate  ;  2,  cohesion  figures ;  3,  equilibrium 
tubes ;  4,  upward  pressure  apparatus ;  5,  brass  bucket  with  accurately  fitting 
solid  piece  of  brass  to  illustrate  the  principle  of  Archimedes  ;  6,  capillary  tubes  ; 
7,  tall  glass  jar,  with  tube  and  funnel ;  8,  stoppered  glass  bottle  ;  9,  barometer 
tube  :  10,  hollow  copper  globe  for  weighing  air,  with  stop-cock  and  scale-beam 
for  suspension  ;  11,  automatic  table  air-pump ;  12,  lifting  and  force  pump ;  13, 
Boyle's  law  apparatus;  14,  siphon;  15.  large-mouth  glass  bottle,  inverted  over 
porous  cup,  from  which  a  glass  tube  dips  into  a  tumbler  of  water.  The  iron 
stand  is  similar  to  that  described  on  page  230.  Teachers  and  pupils  are  referred, 
for  such  of  this  outfit  as  they  can  not  readily  construct  for  themselves,  to  any 
instrument-maker. 


174 


LIQUIDS  AND  GASES. 


EXPERIMENTS. — At  the  middle  of  a  thin  disk  of  metal  or  glass, 
fasten  a  hook  with  solder  or  wax,  as  shown  in  Fig.  73,  or  drive  a  screw- 
eye  into  a  flat  piece  of  wood.  Into  the  hook  or  eye,  loop  a  rubber 
band.  Bend  the  hook  until  the  disk  hangs  truly  horizontal.  Then, 

holding  the  upper  end  of  the  rubber 
in  the  hand,  lower  the  disk  (which 
must  not  be  greasy)  until  it  touches 
a  water  surface.  Pull  carefully 
straight  upward.  You  will  find 
that  you  have  to  pull  quite  hard, 
as  you  perceive  from  the  stretch  of 
the  band,  before  the  disk  tears  away 
from  the  water.  The  water  and 
disk  therefore  adhere.  But  this  ex- 
periment also  illustrates  the  cohe- 
sion of  the  water ;  for,  if  the  parti- 
cles of  water  did  not  hold  together, 
the  disk  would  have  to  lift  merely 
the  weight  of  those  particles  which 
adhered  to  it,  and  would  therefore 
be  no  harder  to  lift  before  it  sepa- 
rated from  the  liquid  than  after- 
ward. In  fact,  what  we  really  do  when  we  pull  the  disk  away  from  the 
liquid,  is  to  tear  apart  the  cohering  water  particles,  and  not  to  pull 
apart  the  water  and  the  disk. 

Dissolve  in  warm  water  about  one  fortieth  of  its  weight  of  pure 
soap.  Filter  through  thin  filter-paper.  Add  about  one  half  the  bulk 
of  glycerine,  and  let  the 
mixture  stand  for  several 
days.  Cool  by  placing  on 
ice,  and  then  filter  a  second 
time.  Next  procure  several 
feet  of  No.  18  or  20  annealed 
iron  wire,  and  make  up,  of  a 
size  of  an  inch  or  more  to 

a  side,  some  of  the  forms  FlG  74.._coHESioN  FIGURES  IN  WIRE  FORMS. 
shown  in  Fig.  74.  Dip  the 

circle  into  the  soap  solution.  On  drawing  it  out,  a  thin  film  will  be 
found  filling  the  circle.  This  illustrates  both  adhesion  and  cohesion. 
How?  Dip  the  other  forms.  They  will  show  when  taken  out  extreme- 
ly interesting  combinations  of  films.  By  breaking  one  or  another  of 
the  several  films  of  the  cube,  peculiar  curved  surfaces  can  be  formed. 


FIG.  73. — ILLUSTRATING  THE  ADHESION 
AND  COHESION  OF  WATER. 


SURFACE  TENSION.  175 

The  tints  of  these  films  are  often  very  beautiful.  Large  bubbles  may 
be  blown  with  this  solution,  and  they  will  illustrate  many  phenomena 
of  cohesion,  color,  etc. 

Surface  Tension. — Let  water  drop  slowly  from  the  end 
of  your  finger.  A  drop  as  it  falls  through  the  air  is  spher- 
ical. Rain-drops  are  also  spherical,  as  you  can  see  by  watch- 
ing closely,  and  as  is  proved  by  the  rainbow  (see  page  368). 
A  drop  of  water  on  an  oily  or  smoked  surface,  or  a  drop  of 
mercury  on  the  table-top,  has  the  form  of  a  sphere.  Why 
is  it  that  these  small  masses  of  liquid  take  this  form  ? 

Remember  that  the  force  of  cohesion  between  the  mol- 
ecules is  very  strong  when  they  are  exceedingly  close  to- 
gether, but  ceases  to  be  sensible  at  even  very  short  distances. 
Let  a,  Fig.  75,  represent  a  molecule  inside  a  mass  of  liquid. 
Then  a  would  feej  the  pull  of  all  the 
molecules  which  are  within  a  certain 
short  distance  of  it,  but  not  of  those  be- 
yond that  limit.  Let  the  small  dotted 
circle  indicate  a  sphere  described  about 
a  as  a  center,  at  such  a  distance  that 
the  attraction  on  a  of  all  molecules  in- 
side the  sphere  is  sensible,  but  that  of  FTG-  TS.-SPHERE  OF 

.,  .    .  ,      .      .  M  i         •  -i  ATTRACTION. 

those  outside  is  insensible — i.  e.,  is  less 
than  some  specified  small  amount.  This  sphere  is  called 
the  sphere  of  attraction  of  a.  For  water,  the  radius  of  this 
sphere — i.  e.,  the  distance  at  which  cohesion  ceases  to  be 
sensible — is  about  two  millionths  of  an  inch.  Now  there 
would  be  the  same  number  of  molecules  on  all  sides  of  a 
within  its  sphere  of  attraction;  hence  a  would  be  equally 
pulled  in  all  directions,  and  cohesion  would  not,  therefore, 
tend  to  move  it  in  any  one  direction  more  than  another. 

Suppose  now  that  we  have  a  drop  of  water  represented  as  highly 
magnified  by  the  outside  circle  of  Fig.  75.  Let  the  large  dotted  circle 
be  drawn  so  that  its  distance  from  the  outer  one  is  just  equal  to  the 
radius  of  the  sphere  of  attraction  (two  millionths  of  an  inch).  Any 
molecule  lying  inside  this  dotted  circle  will  then  be  equally  pulled  in 


176  LIQUIDS  AND  GASES. 

all  directions.  But  for  all  molecules,  for  instance,  c  and  d,  lying  be- 
tween this  and  the  surface  of  the  drop,  there  will  be  no  molecules  in 
those  parts  of  their  spheres  of  attraction  which  are  outside  the  drop 
surface.  Hence  all  molecules  near  the  surface  will  be  more  strongly 
attracted  toward  the  interior  of  the  drop  than  toward  its  surface,  and 
for  those  molecules  very  close  to  and  at  the  surface,  the  pull  will  be 
very  strong.  This  is  true  of  every  free  liquid  surface  (i.  e.,  not  bounded 
by  a  solid  or  other  liquid).  Thus  the  surface  molecules  are  under  a 
strong  inward  pull,  and  form  a  sort  of  skin  over  the  drop,  which  acts 
like  a  stretched  elastic  bag,  as  in  a  toy  balloon.  The  surface  of  a 
liquid,  therefore,  acts  as  if  it  were  under  a  continuous  pull  or  ten- 
sion ;  it  is  therefore  said  to  have  a  Surface  Tension.  By  this  surface 
tension  the  liquid  is  forced  to  take  that  shape  which  gives  the  least 
surface  for  the  given  volume  of  liquid,  and  that  shape  is  a  sphere. 

A  perfectly  spherical  form  is  not  attained  by  a  drop  lying  on  a 
solid  surface,  because  the  weight  is  great  as  compared  with  the  cohe- 
sive force,  and  flattens  the  drop  out.  The  rounded  form  of  a  drop  of 
melted  wax,  of  the  softened  end  of  a  melted  stick  of  sealing-wax  or  of 
a  glass  tube  or  rod,  of  a  soap-bubble,  etc.,  is  due  to  the  action  of  the 
surface  tension,  as  are  also  the  phenomena  of  capillarity  about  to  be 
described.  Solid  surfaces  also  must  possess  a  surface  tension,  but  its 
effects  are  seldom  perceptible. 

Annealing. — A  similar  condition  of  surface  tension  is 
exhibited  by  "  Prince  Rupert  drops,"  which  are  made  by 
allowing  drops  of  molten  glass  to  fall  into  water.  The  outer 
surface  of  a  drop  is  thus  suddenly  hardened,  while  the  interior 
remains  liquid.  As  the  interior  gradually  solidifies,  it  con- 
tracts, putting  the  surface  layers  of  solidified  glass  under 
great  stress.  If  the  surface  is  scratched  or  cut,  the  crack 
thus  started  is  violently  spread  by  this  stress  in  many  direc- 
tions, and  the  drop  flies  instantly  into  fragments.  This 
strained  condition,  due  to  sudden  cooling,  may  be  reduced 
or  avoided  by  the  process  of  Annealing — i.  e.,  by  slow 
cooling  either  at  the  time  of  making  or  after  subsequent 
heating.  Most  glassware  has  to  be  annealed.  To  produce 
homogeneous  and  unstrained  or  evenly  strained  glass  for 
large  telescope  lenses,  extraordinary  pains  are  taken  in  the 
annealing  process. 


CAPILLARITY. 


177 


FIG.  76. 


ft 


FlG.  77. — CAPILLARITY  ILLUSTRATED  BY 
GLASS  PISTES. 


Capillarity. — If  you  dip  a  clean  glass  plate 
into  a  dish  of  water,  the  water  will  rise  up  at 
the  surface  of  the  plate  in  the  curves  C  and  D 
(Fig.  76)  instead  of  lying  flat.  This  is  because 
the  adhesion  of  the  water  to  the  glass  much 
exceeds  the  cohesion  of  the  liquid. 

EXPERIMENTS.— Hold  two  glass  plates  with  their  edges  together  at 
A,  but  kept  a  very  little  apart  at  B  by  a  bit  of  wire  or  string  (Fig.  77). 

Dip  the  lower  edge  of  the  combina- 
tion into  water,  and  the  liquid  will 
rise  in  the  form  of  the  curve  shown 
in  the  figure. 

Obtain  a  clean  glass  tube  of 
about  a  tenth  of  an  inch  in  diame- 
ter. Dip  it  vertically  into  water. 
The  water  will  rise  in  the  tube. 
Try  finer  tubes.  The  finer  the 
tube,  the  higher  the  water  will  rise. 

Fine  tubes  are  called  capillary  tubes  (from  the  Latin 
capillus,  a  hair),  because  of  their  hair-like  bore.  From  the 
fact  that  the  action  just  illustrated  is  easily  seen  in  these 
capillary  tubes,  the  phenomenon  is  called  Capillarity. 

In  a  glass  tube  one  tenth  of  an  inch  in  inside  diameter, 
water  will  rise  to  a  height  of  a  little  more  than  one  quarter 
of  an  inch.  The  height  for  the  same 
liquid  is  inversely  as  the  diameter  of  the 
tube,  but  varies  with  the  liquid.  Thus 
in  a  tube  of  O01  inch  diameter,  water 
will  rise  0-1  -r-  0-01  =  10  times  as  high 
as  in  one  Ol  inch  diameter,  or  10  x  0-25 
=  2*5  inches. 

Liquids  will  not  overflow  a  tube  by 
capillary  action.  If  a  tube  O'Ol  inch 
diameter  were  dipped  into  water  until  it  projected  only 
half  an  inch,  the  water  would  rise  to  the  top  of  the  tube 
and  stop,  because  of  the  change  in  form  of  the  tube  at  that 
point. 


FIG.  78. -WATER.  IN 
CAPILLARY  TUBES. 


ITS 


LIQUIDS  AND  GASES. 


FIG.  79. — MERCURY  IN 
CAPILLARY  TUBES. 


Water  and  most  liquids  adhere  to  glass  and  other  solids 
more  strongly  than  they  cohere.  But  this  is  not  true  of  mer- 
cury, which  adheres  to  glass  less  strongly  than  it  coheres. 

EXPERIMENT. — Dip  the  glass  plate  when  thoroughly  dry  into  mer- 

oury ;  the  curves  at  the  contact  will  be  downward  instead  of  upward. 

Fig.  79  shows  the  action  of  mercury  if 
the  capillary  tubes  of  Fig.  78  were  plunged 
into  it.  The  cohesion  of  the  mercury  is  so 
much  greater  than  the  adhesion  to  the  glass 
that  the  mercury  does  not  wet  the  glass  like 
water,  but  assumes  a  convex  form,  as  water 
does  upon  a  smoked  or  greasy  surface. 

The  toy  called  a  "sucker"  is  a  round 
piece  of  leather  with  a  string  fastened  to  the 
middle.  If  it  be  thoroughly  we^  and  pressed 
firmly  down  upon  a  flat  stone,  some  water 

will  be  squeezed  out  of  the  leather  and  form  a  film  bett^en  it  and  the 

stone,  forcing  the  air  out.     If  the  string  be  now  carefully  pulled,  the 

stone,   even  if    quite    heavy,   will    be 

lifted.    This  is  due  to  the  combined 

action  of  capillarity  and  atmospheric 

pressure.    The  adhesion  of  the  water 

to  the  stone  and  the  cohesion  of  the 

water  enable  the  concave  surface,  C,  of 

the  film  to  sustain  a  part  of  the  atmos- 
pheric pressure.     Thus  the  intensity 

of  the  pressure  within  the  water  and 

tending  to  separate  the  sucker  from 

the  stone  is  less  than  the  intensity  of 

the  external  atmospheric  pressure  on 

the  upper  side  of  the  sucker,  tending 

to    hold    sucker    and  stone   together. 

Therefore,  if  the  water -film  be  thin 

enough  at  C,  and    the   sucker   large 

enough,  there  may  be  a  resultant  pressure  sufficient  to  equal  or  ex- 
ceed the  weight  of  the  stone,  so  that  it  can  be  lifted. 

Porous  Objects  absorb  Liquids  by  Capillary  Ac- 
tion.— Pores  form  irregular  spaces,  into  which  liquids  rise  or 
flow  just  as  water  rises  in  capillary  tubes.  Blotting-paper, 
a  lump  of  sugar,  a  lamp-wick,  absorb  liquids  in  this  way. 


80.— PRINCIPLE  OP  THE 
SUCKER. 


DIFFUSION  OF  LIQUIDS. 


1Y9 


But  you  will  remember  that  the  cause  of  this  action  lies 
wholly  at  the  surface  of  the  liquid,  and  that  as  a  rule  the 
liquid  can  not  be  made  to  overflow.  Therefore,  a  con- 
tinuous flow  of  liquid  can  not  be  due  to  capillarity  unless 
the  liquid  is  evaporated  or  otherwise  removed  from  the  sur- 
face, as,  for  instance,  in  the  case  of  a  lamp-wick. 

Compressibility. — By  very  exact  experiments,  it  has 
been  shown  that  liquids  are  compressible — i.  e.,  that  their 
volumes  may  be  reduced  when  under  pressure.  Water  is 
only  very  slightly  compressible,  even  with  enormous  pressure. 

Diffusion. — Pour  into  a  tall  glass  jar  or  bottle  enough 
water  to  fill  it  two  thirds  full.  Through  a  funnel  and  long 
tube  reaching  to  the  bottom,  introduce  carefully  about  one 
third  as  much  of  a  nearly  saturated  solution  of  blue  vitriol. 
Let  the  glass  stand  without  dis- 
turbance for  several  days.  You 
will  see  that  at  first  the  surface 
between  the  blue  solution  and  the 
water  is  sharply  defined.  Soon  it 
becomes  blurred,  and  gradually  the 
vitriol  spreads  up  through  the  liquid 
until  the  whole  becomes  of  a  uni- 
form tint. 

This  process  is  called  Free  Dif- 
fusion. It  is  due  to  the  fact  already 
stated  (page  167)  that  the  molecules 
move  about  from  one  part  to  an- 
other of  the  body  of  a  liquid. 

EXPERIMENTS. — Into  a  similar  jar  put 
a  solution  of  blue  litmus  in  place  of  the 
water,  and  then  pour  in  through  the  fun- 
nel a  small  amount  of  sulphuric  acid.  In 

the  course  of  two  dayt,  the  sulphuric  acid    ™ 

•ni          i  ,.„:  FIG.  81.— DIFFUSION  OF  LIQUIDS. 

will  have  become  diffused  throughout  the 

liquid.    This  will  be  known  from  the  change  of  color,  for  acids  turn  blue 
litmus  red.     The  progress  of  the  diffusion  can  thus  be  easily  followed. 


180 


LIQUIDS  AND  GASES. 


Place  some  blue  vitriol  solution  in  a  porous  cup,  such  as  is  used  in 
some  electric  batteries.  Stand  the  cup  in  a  dish  of  water,  but  with  its 
top  out.  The  blue  vitriol  will  diffuse  through  the  cup  into  the  water. 
A  similar  experiment  may  be  made  with  the  acid  and  litmus.  This 
diffusion  through  porous  partitions  is  not  different  in  character  from 
the  free  or  direct  diffusion,  but  the  principle  is  made  practical  use  of 
in  many  ways. 

Kate  of  Diffusion. — Some  substances  diffuse  rapidly, 
others  very  slowly.  Most  of  those  solids  which  diffuse  rap- 
idly when  in  solution  are  such  as  have  a  distinctly  crystal- 
line form,  such  as  common  salt,  sulphate  of  magnesium, 
etc.  This  class  is  therefore  called  crystalloids. 

Of  the  substances  which  diffuse  very  slowly  or  hardly  at 
all,  gelatine,  starch,  dextrine,  and  gums  are  examples.  They 
all  form,  when  moist,  more  or  less  gelatinous  or  glue-like 
masses,  and  are  therefore  called  colloids  (from  a  Greek  word 
for  glue).  The  reason  why  the  colloids  diffuse  so  much  more 
slowly,  is  probably  because  their  molecules  are  very  large  as 

compared  with  those 
of  the  crystalloids, 
the  size  being  due 
to  the  fact  that  the 
molecules  consist  of 
a  large  number  of 
atoms.  The  different 
rates  of  diffusion  are 
utilized  in  separat- 
ing substances  from 
a  mixed  solution. 

Osmosis. — Tie  a 

piece  of  moistened 
bladder,  frog-skin,  or 
other  animal  mem- 

FIG.  82.— DIFFUSION  THROUGH  ANIMAL  MEMBRANE,    i  nvpr    thp   end 

of  a  funnel  A  (Fig.  82).     Fill  the  funnel  with  a  strong  solu- 
tion of  blue  vitriol  or  sugar.     Invert  it  in  a  dish  of  water,  B, 


OSMOSIS. 

by  means  of  a  clamp.  Note  the  height  0  at  which  the 
solution  stands  at  the  outset.  After  an  hour  or  two,  the 
liquid  at  C  will  be  found  higher  than  at  the  start,  show- 
ing that  more  of  the  liquid  has  diffused  from  B  into  A 
than  from  A  into  B ;  but  the  color  (or  taste)  of  the  liquid 
in  B  will  prove  that  some  liquid  has  also  diffused  from 
AtoB. 

Thus  liquids  and  solids  in  solution  diffuse  through  ani- 
mal membranes.  But  such  membranes  as  the  bladder  are 
different  in  structure  from  the  porous  cup  of  the  former 
experiment ;  they  contain  no  pores  which  can  be  discov- 
ered even  with  a  powerful  microscope.  Hence  it  is  not 
strange  that  the  process  of  diffusion  through  such  mem- 
branes, which  is  called  Osmo'sis,  follows  different  laws  from 
free  diffusion  or  diffusion  through  porous  substances,  and 
depends  on  the  nature  of  the  membranes  used.  Osmosis 
has  important  practical  applications.  It  also  enters  largely 
into  the  operations  of  Nature,  causing,  for  instance,  the 
ascent  and  descent  of  sap  in  trees  and  vines. 


QUESTIONS.— Show  that  cohesion  and  adhesion  exist  in  liquids.  What  is  surface 
tension  ?  To  what  is  it  due  ?  Describe  it  in  detail.  What  is  meant  by  the 
sphere  of  attraction  ?  At  how  great  a  distance  does  the  cohesion  of  water 
cease  to  be  sensible  ?  Why  do  rain-drops  assume  a  spherical  form  ?  What  do 
the  Prince  Rupert  drops  illustrate  ?  How  are  they  made  ?  What  is  the  process 
of  annealing  ? 

To  what  phenomena  is  the  name  Capillarity  given  ?  Describe  several  experi- 
ments illustrating  it.  How  high  would  water  rise  in  a  tube  of  0'03  inch  bore  ? 
Will  liquids  overflow  in  capillary  tubes  ?  Why  not  ?  Why  does  oil  rise  in  a 
lamp-wick  ?  If  the  end  of  a  piece  of  dry  wood  is  dipped  into  water,  why  does 
the  water  rise  in  the  wood  ?  What  is  necessary  in  order  that  a  liquid  should 
wet  a  solid  ?  Describe  the  action  of  mercury  in  fine  tubes.  Why  does  it  act  in 
this  way  ?  Describe  and  explain  the  action  of  the  toy  called  the  "  sucker." 

Are  liquids  compressible  ?  Describe  an  experiment  illustrating  the  free  diffusion 
of  liquids.  One  illustrating  diffusion  through  porous  substances.  What  is  the 
molecular  explanation  of  the  process  of  free  diffusion  ?  What  is  the  difference 
between  crystalloids  and  colloids  ?  Describe  an  experiment  showing  the  phe- 
nomenon of  Osmosis.  Are  the  laws  of  osmosis  different  from  those  of  free 
diffusion  and  of  diffusion  through  porous  partitions  ?  For  what  reason  ? 


182  LIQUIDS  AND   GASES. 

PRESSURE  OF  LIQUIDS. 

Hydrostatics.  —  Hydraulics.  —  Hydrostat'ics  is  the 
name  given  to  that  branch  of  Physics  which  deals  with 
liquids  at  rest ;  Hydraulics,  to  that  branch  which  has  to  do 
with  liquids  in  motion. 

Hydrostatic  Law  of  Transmission  of  Pressure. — 

In  the  case  of  a  mass  of  liquid  at  rest,  a  pressure  exerted  at 
any  point  is  transmitted  equally  in  all  directions  through- 
out the  liquid. 

Fig.  83  represents  a  vessel  filled  up  to  a  b  with  any  liquid,  and  a  b 
is  a  piston  which  can  be  forced  down  by  pressure.     Suppose,  for  exam- 
ple, this  pressure  to  be  equivalent  to  2  pounds  on  each  square  inch  of 
the  surface  of  the  piston.     Then  it  will  be  transmitted 
through  the  liquid  in  every  direction,  so  that  on  each 
square  inch  of  the  walls  of  the  vessel,  e.  g.,  at  F,  E,  D,  C, 
or  anywhere  else,  there  will  also  be  a  pressure  of  2  pounds 
to  the  square  inch,  if  we  neglect  for  the  present  the 
weight  of  the  liquid  itself.     Further,  if  we  were  to  put 
into  the  liquid  a  sheet  of  metal  or  any  object  whatever 
of  any  size  or  shape,  there  would  be  a  pressure  of  2 
pounds  on  each  square  inch  of  its  surface.     Or,  if  we 
think  of  any  two  parts  of  the  liquid  as  separated  by  an 
imaginary  plane  moving  in  any  direction,  then  upon  each 
side  of  this  plane  there  will  be  a  pressure  of  2  pounds  to  the  square 
inch.     The  pressure  is  thus  the  same  through  all  parts  of  the  liquid, 
and  at  every  point  it  is  equal  in  every  direction. 

Of  course,  you  can  see  that  it  must  be  equal  in  every 
direction ;  for  if  it  were  greater  in  any  one  direction  than 
in  another,  then  there  would  be  an  unbalanced  force,  and 
the  liquid  at  that  point  would  move  in  the  direction  of  that 
force.  But  we  are  considering  a  liquid  at  rest.  Hence  the 
pressure  must  be  equal  in  all  directions.  For  the  same 
reason,  too,  it  must  be  equal  at  all  points  of  the  liquid.  If 
it  were  less  at  one  point  than  at  another  (leaving  out  of 
consideration  the  effect  of  weight),  there  would  be  motion 
toward  the  point  where  the  pressure  was  less. 


TRANSMISSION  OF  PRESSURE.  183 

In  order  to  understand  how  pressure  is  transmitted  according  to 
this  law,  let  us  imagine  what  takes  place  among  the  molecules.  Re- 
member that  the  number  of  molecules  is  enormously  large,  and  that 
they  are  excessively  minute,  so  that  we  never  perceive  anything  but 
the  average  effect  of  a  vast  number  of  them.  We  have  seen  (page  57) 
how  a  continuous  force  or  pressure  on  a  surface  can  be  produced  by  a 
bombardment  of  balls  or  molecules.  The  pressure  of  liquids  or  gases 
upon  the  walls  of  the  vessels  inclosing  them  is  of  this  nature,  being 
due  simply  to  the  battering  of  those  surfaces  by  the  molecules  of  the 
fluids.  The  molecules  strike  the  surfaces  and  rebound  with  equal 
velocities,  but  in  a  reversed  or  changed  direction.  This  reversal  of 
the  direction  of  their  momentum  produces  the  pressure — i.  e.,  the  tend- 
ency to  acceleration — on  the  walls. 

If  the  number  of  molecules  happens  to  be  greater  in  a  given  volume 
near  one  point  of  the  surface,  then  the  number  of  molecules  striking 
upon  the  surface  in  a  unit  of  time  is  greater,  and  therefore  the  pressure 
is  greater ;  or  if  the  velocity  of  the  molecules  is  increased,  each  will 
strike  a  harder  blow,  and  thus  the  pressure  will  be  greater.  If  the 
pressure  is  increased  at  any  point  of  the  liquid,  as  by  pressing  harder 
on  the  piston  a  b,  in  Fig.  83,  then  the  molecules  become  more  crowded 
together  at  that  point,  and  therefore  strike  harder  against  their  neigh- 
bors, and  these  in  turn  against  theirs,  forcing  them  back  in  all  direc- 
tions until  the  pressure  is  equal  everywhere.  If  you  think  of  the 
pressure  always  as  caused  by  this  battering  or  bombarding  of  the 
molecules,  and  of  its  transmission  through  the  liquid  as  due  to  the 
jostling  of  the  molecules  against  one  another,  you  will  find  it  easier  to 
comprehend  many  of  the  phenomena. 

The  Equal  Transmission  of  Pressure  in  all  Direc- 
tions may  be  illustrated  by  simple  experiments.  If,  in  an 
apparatus  such  as  that  of  Fig. 
82,  holes  are  made  at  any  points, 
the  liquid  will  be  forced  out. 
With  a  suitable  measuring  in- 
strument attached  to  each  of  the 
holes,  the  same  pressure  will  be 
indicated.  If  the  finger  be  placed 
over  the  end  of  the  water-faucet, 
the  jet  can  be  made  to  play  equally 
in  any  direction.  Through  holes  in  the  garden  hose  the 


184  LIQUIDS  AND   GASES. 

water  will  pass  out  with  equal  force  upward,  downward,  or 
sidewise. 

Pressure  per  Unit  Area. — Intensity  of  Pressure. — 

In  the  case  of  liquids  and  gases,  we  have  to  deal  with  press- 
ures distributed  over  considerable  areas.  Hence,  when  we 
wish  to  be  definite,  we  must  speak  of  the  amount  of  force 
on  a  unit  area.  This  is  called  the  intensity  of  the  pressure, 
or  more  often  merely  "the  pressure." 

The  total  pressure  on  any  surface  will  then  be  equal  to  the  inten- 
sity of  the  pressure  multiplied  by  the  area  of  the  surface.  For  in- 
stance, if  the  intensity  of  the  pressure  is  5  pounds  per  square  inch, 
and  the  surface  acted  upon  is  10  square  inches,  the  total  pressure  is 
5  x  10  =  50  pounds.  This  is  clear  when  you  think  that  the  pressure 
depends  only  on  the  number  of  particles  battering  the  surface,  which 
would  naturally  be  twice  as  great  with  twice  the  surface,  three  times 
with  thrice  the  surface,  and  so  on. 

Pressure  due  to  Weight  of  Liquid. — In  the  case  of 

the  vessel  full  of  shot  (Fig.  20,  page  73),  you  can  under- 
stand that  the  upper  layer  would  press  upon  the  second  with 
a  force  equal  to  its  weight,  the  second  on  the  third  with  a 
force  equal  to  the  sum  of  the  weight  of  the  first  two,  and  so 
on.  Imagine  now  the  shot  to  be  liquid  molecules  flying  about 
in  all  directions,  and  thus  perfectly  free  to  move.  You  will 
then  see  that  the  particles  will  press  against  the  side  at  any 
point  just  as  hard  as  they  press  downward  at  the  same  level ; 
that  is,  the  intensity  of  the  pressure  will  be  the  same  on  the 
side  of  the  vessel  as  in  a  downward  or  any  other  direction. 
Where  the  depth  is  twice  as  great,  the  intensity  of  the 
pressure  will  be  twice  as  great,  etc. ;  that  is,  the  intensity  of 
the  pressure  is  proportional  to  the  depth. 

The  greater  intensity  of  pressure  may  be  pictured  as  due  to  a 
greater  bombardment  of  molecules.  This  arises  from  the  compression 
of  the  liquid,  which,  although  slight,  is  enough  to  bring  into  each  unit 
of  volume  of  the  liquid  an  enormous  number  more  of  molecules,  and 
thus  to  produce  the  increased  number  of  blows  on  the  unit  of  surface. 

At  great  depths,  the  pressure  of  water  becomes  immense ;  for  this 


PRESSURE  BY   WEIGHT  OF  LIQUID.  185 

reason,  divers  do  not  care  to  descend  more  than  a  hundred  feet.  Glass 
bottles,  empty  and  tightly  corked,  are  often  let  down  with  cords  at 
sea,  and  the  pressure  is  generally  sufficient  to  crush  them  at  compara- 
tively slight  depths.  If  the  bottles  do  not  break,  the  corks  are  driven 
in  or  water  is  forced  through  the  pores.  When  a  ship  goes  down  at 
sea,  her  timbers  are  seldom  seen  again.  By  reason  of  the  great  press- 
ure, capillarity,  diffusion,  etc.,  the  pores  of  the  submerged  wood  be- 
come filled  with  water  instead  of  air.  Hence,  since  the  solid  portions 
of  wood  are  denser  than  water,  the  sunken  vessel  can  not  rise. 

The  Intensity  of  the  Pressure  does  not  depend 
on  the  Form  of  the  Vessel,  but  only  on  its  depth ;  for,  if 
any  molecule  is  pressed  upon,  it  transmits  the  pressure  in  all 
directions.  If  the  pressure  of  the  first  layer  is  transmitted 
to  any  one  molecule  of  the  next,  then  such  molecule  will 
jostle  about  until  all  the  molecules  in  that  layer  have  the 
same  pressure.  For  the  transmission  of  pressure,  then,  it  is 
merely  necessary  that  there  should  be  some  communication, 
however  small,  between  successive  layers. 

Thus,  suppose  Fig.  85  to  represent  a  cavity  in  the  ground  filled 
with  water.  The  pressure  at  any  point  C  will  be  the  same — whatever 
the  number  or  size  of  the  various  parts  of  the  channel  A  B  communi- 
cating with  B— and  will  depend  merely  on  the  vertical  depth  of  C 
below  the  surface.  Further,  the 
pressure  on  every  unit  of  area  at  the 
same  level  is  the  same.  This  is  true 
only  when  water  is  not  flowing 
through  A  B,  but  is  standing  still  in 
the  entire  cavity ;  otherwise,  friction 
makes  some  difference  as  in  all  cases 
of  motion. 

The  pressure  on  a  unit  area  at  C, 
then — say  on  one  square  foot — would 
be  just  the  same  as  if  a  straight  pipe,      FlG-  85-— PRESSURE  PROPORTIONAL 
one  square  foot  in  section,   passed  T°  DEPTH> 

directly  upward  from  C  to  the  surface  and  were  filled  with  water. 
The  pressure  on  one  square  foot  at  the  bottom  of  such  -a  pipe  would 
be  62-5  pounds  for  each  foot  of  depth— i.  e.,  in  all  62-5  x  depth,  for 
one  cubic  foot  of  water  weighs  about  62-5  pounds.  Hence  the  fol- 
lowing rules : 
13 


186  LIQUIDS  AND  GASES. 

To  find  the  intensity  of  pressure  in  pounds  per  square 
foot  due  to  water  at  any  depth,  d,  multiply  depth  in  feet  by 
62-5— i.  e.,  find  62-5  X  d. 

To  find  the  total  pressure  on  any  surface  of  area  a  at 
depth  d,  multiply  intensity  of  pressure  by  area— i.  e ,  find 
62-5  X  d  X  a. 

To  find  the  average  intensity  of  pressure  on  any  rect- 
angular plane  surface,  multiply  depth  d'  of  middle  of  sur- 
face by  62-5— i.  e.,  find  62-5  X  d'. 

To  find  the  total  pressure  on  such  surface,  multiply  the 
average  intensity  by  the  area — i.  e.,  find  62-5  X  d'  X  a. 

If  the  liquid  be  other  than  water,  use  instead  of  62-5  the  weight 
in  pounds  of  a  cubic  foot  of  the  liquid.  What  would  be  the  pressure 
per  square  inch  at  the  bottom  of  a  column  of  mercury  30  inches  high, 
mercury  being  13-6  times  as  dense  as  water?  The  cubic  foot  of  mer- 
cury would  weigh  13'6  x  62*5  pounds  =  850  pounds.  The  pressure 

on 

on  a  square  foot  at  a  depth  of  30  inches  (y^  =  2-5  feet)  would  be  850 

2  125 
x  2*5  =  2,125  pounds,  or  per  square  inch  =    '       =  14*76  pounds  per 

144 

square  inch.  How  high  a  column  of  water  would  be  necessary  to  pro- 
duce the  same  pressure  per  square  inch  t  As  mercury  is  13'6  times  as 
dense  as  water,  a  column  of  water  13-6  times  as  high  would  be  necessary 
to  produce  the  same  pressure — i.  e.,  13*6  x  2*5  =  34'0  feet. 

It  follows  from  the  statements  of 
this  section  that  any  pressure  may  be 
measured  by  the  vertical  height  of  a 
column  of  liquid  which  it  will  sustain 
against  gravity. 

Upward  Pressure. — From  what 
has  been  shown,  it  follows  that  if 
m  n  represent  a  sheet  of  metal  or 
H  any  substance  in  a  mass  of  liquid, 
FIG.  86.— METAL  PLATE  UNDER  then  m  n  is  pressed  from  each  side 
WATER.  wifh  equal  force.      If  mn  happens 

to  be  horizontal,  it  will  be  pressed  upward  and  downward 
equally  by  the  liquid.  If  it  is  vertical,  it  will  be  pressed 


UPWARD   PRESSURE   OF   LIQUIDS. 


187 


equally  to  right  and  left,  and  so  on.  The  pressure  on  either 
side  would  be  perceptible,  if  we  could  remove  the  pressure 
from  the  opposite  side. 

This  may  be  accomplished  by  the  ar- 
rangement shown  in  Fig.  87.  The  ground 
glass  attached  to  the  string  fits  the  lower 
surface  of  the  tube  closely.  Hold  the  plate 
up  by  the  string  against  the  tube,  and 
thrust  the  whole  nearly  to  the  bottom  of 
the  water.  Then  let  go  the  string,  and  the 
upward  pressure  will  hold  the  plate  against 
the  tube.  If  the  tube  be  raised,  the  press- 
ure will  gradually  diminish,  until  near  the 
top  it  becomes  too  slight  to  support  the 
weight  of  the  plate,  which,  therefore,  drops 
off.  Hold  an  empty  bpttle  neck  upward  in 
the  hand  and  press  it  down  in  water.  You 
will  perceive  very  much  better  than  by  the 
foregoing  experiment  how  much  pressure 
there  is  upward  on  the  bottom  of  the  bot- 
tle, and  how  the  pressure  increases  as  you 

push  the  bottle  down. 

FIG.  87.— UPWARD  PRESSURE 

The  Upper  Surface  of  a  Liquid  APPARATUS. 

at  Rest  is  level.— If  C  P  D  (Fig.  88)  be  the  surface  of  a 
liquid  standing  in  any  receptacle,  and  not  level,  then  any 
point  P  will  at  once  begin  to  move,  for  it  is  acted  upon  by 
its  weight  in  the  direction  W.  This  force 
may  be  resolved  into  two  components,  A 
and  B,  the  latter  perpendicular  to  the  surface 
at  the  point,  and  therefore  balanced,  the 
other  tangent  to  the  surface,  and  thus  in 
a  direction  in  which  the  particle  P  can  freely 
move.  Such  action  will  continue  until  no  point  is  higher 
than  any  other,  and  the  surface  thus  becomes  level. 

Level  in  Communicating  Vessels. — Let  A  B  be  any 

vessel  having  a  partition  E  D  separating  it  into  two  parts. 
Put  the  same  kind  of  liquid  into  the  two  sides,  but  to  a 


FIG.  88. 


188 


LIQUIDS  AND  GASES. 


greater  height  A  on  one  side  than  B  on  the  other.  At  any 
point,  the  partition  will  receive  a  greater  pressure  on  the  A 
side  than  on  the  B  side,  because  of  the  greater  depth  of 
liquid.  Make  a  hole  through  D  E  at 
any  point  D  below  B.  Owing  to  the 
greater  pressure  on  the  A  side,  the 
liquid  must  be  forced  into  the  B  side, 
and  this  action  will  continue  until  the 
pressure  from  A  toward  B  and  that 
FIG.  89.-CHANGE  OP  LEVEL  from  B  toward  A  are  equal.  But  this 
can  be  only  when  the  depths  of  liquid 
are  the  same  in  both  sides.  Hence,  when  the  liquid  is  at  rest 
in  the  two  communicating  parts  of  the  vessel,  both  surfaces 
must  be  at  the  same  level,  F  G.  This  is  obviously  only  a  special 
case  of  the  principle  explained  in  the  foregoing  paragraph. 

The  same  statement  must  evidently  hold  true  for  any  set  of  com- 
municating open  vessels,  whatever  their  form  and  size,  as,  for  example, 
the  system   shown  in 
Fig.  90.    The  ordinary 
glass  water-gauge  used 
on    steam-boilers   for 
showing  the  height  of 
water  in  the  boiler,  is 
an  application  of  this 
principle. 

The  law  that  water 
seeks  its  own  level  is 
not  true  for  vessels  in 
which  the  elevation  or  depression  due  to  capillarity  is  perceptible,  01 
for  tubes  in  which  friction  interferes  with  the  free  flow  of  the  liquid. 

The  Spirit-Level  is  an  instrument  used  by  surveyors, 
carpenters,  masons,  and  others,  and  in  scientific  work  by 
physicists  and  astronomers,  to  adjust  lines  or  surfaces.  It 
consists  of  a  glass  tube  nearly  filled  with  alcohol,  or  a  mixt- 
ure of  alcohol  and  ether,  so  as  to  leave  sufficient  air  to  form 
a  small  bubble.  The  tube  is  then  sealed,  and  mounted  in  a 
suitable  wooden  or  metal  case. 


FIG.  90. — EQUILIBRIUM  TUBES. 


THE  HYDRAULIC   PRESS. 


189 


FIG.  91.— SECTION  OP  SPIRIT-LEVEL. 


lib. 


The  mounted  level  is  then  marked  with  a  scale  upon  its 
top,  so  that,  when  the  base  is  perfectly  horizontal,  the  air- 
bubble  will  rest  in  the 
middle  of  the  scale.  If 
the  bubble  comes  to  rest 
in  any  different  posi- 
tion, it  shows  that  one 
end  of  the  glass  tube  is  higher  than  the  other,  and  conse- 
quently that  the  surface  on  which  the  instrument  stands  is 
not  level. 

Hydraulic  Press — Let  A  B  and  D  G,  Fig.  92,  be  two 
upright  cylinders  communicating  by  a  small  tube  C,  and 
containing  water  or  other  liquid.  Let  A  and  E  be  pistons 
working  without  leak  in  the  cylinders.  Neglect  for  the 
present  the  effect  of  friction  and  the  weight  of  the  liquid. 
Assume  the  area  of  A  to  be  one  square 
inch,  and  that  of  E  to  be  one  hundred 
square  inches.  Suppose  that  A  is 
forced  down  one  inch.  Then  E  must 
rise  just  -^  inch ;  for  by  forcing  down 
A  one  inch,  one  cubic  inch  of  liquid 
is  forced  into  D,  and  E  must  rise 
sufficiently  to  admit  this  cubic  inch, 
or,  as  its  area  is  100  square  inches,  it 
must  rise  ^-J-g-  inch.  Then,  by  the 
principle  of  conservation  of  energy, 
if  a  load  of  1  pound  is  put  on  A  and 
descends  through  1  inch,  it  will  be  just  capable  of  moving 
E  up  yi-g-  of  an  inch,  if  its  load  is  100  pounds. 

In  general,  the  total  force  produced  by  E  is  to  that  exerted  upon 
A  as  the  area  of  E  is  to  that  of  A ;  for  let  s  be  the  distance  through 
which  A  descends,  and  /  the  load  upon  it,  and  let  S  be  the  height 
through  which  E  rises,  and  F  the  load  upon  it.  Then  /  X  s  =  F  X  S, 
fs  being  the  work  done  by  /,  and  FS  the  work  done  against  F .-.  F  :  / 
=  s  :  S.  But  if  a  is  the  area  of  A,  and  e  that  of  E,  it  may  be  shown 
as  above  that  s :  S  =  e  :  a  .-.  F  :  /=  e  :  a.  That  is,  the  forces  are  pro- 
portional to  the  piston  areas. 


FIG.  92.— PRINCIPLE  OP 
HYDRAULIC  PRESS. 


190  LIQUIDS  AND  GASES. 

This  arrangement,  then,  constitutes  a  machine  by  which 
we  gain  a  mechanical  advantage  similar  to  that  of  the  lever. 
We  may,  by  making  a  small  force  work  through  a  long  dis- 
tance, produce  a  great  force  which  will  do  an  equivalent 
amount  of  work  through  a  short  distance. 

Such   is   the  Principle  of  the   Hydraulic   Press, 

which,  by  the  use  of  levers  and  a  small  piston  on  the  pump, 
and  of  a  large  piston  at  E,  is  made  to  give  total  pressures  of 
many  tons.  It  is  extensively  used  for  lifting  exceedingly 
heavy  weights,  for  compressing  cotton  and  hay  into  bales, 
for  extracting  the  juices  from  cotton-seed,  etc. 

Fig.  93  illustrates  a  hydraulic  press  of  great  power.  By  inspect- 
ing a  railroad  car,  you  will  see  that  the  wheel  is  firmly  attached  to  the 
axle  and  turns  with  it,  the  bearing  being  on  a  prolongation  of  the  axle 
outside  the  wheel.  The  wheel  is  secured  in  place  upon  the  axle  by 
making  the  latter  about  O'Ol  inch  larger  in  diameter  than  the  corre- 
sponding hole  in  the  wheel,  and  forcing  it  in  by  great  pressure.  When 
thus  joined,  they  hold  together  almost  as  solidly  as  if  of  one  piece  of 


FIG.  93.— SELLER'S  HYDRAULIC  WHEEL-PRESS  FOR  LOCOMOTIVE  DRIVING-WHEELS. 

metal,  and  are  said  never  to  come  apart  in  use.  The  axle  is  suspended 
horizontally  between  C  and  D  by  a  chain  from  the  carriage  E.  The 
wheel  is  held  in  place  at  the  end  of  the  axle  at  D,  and  the  press  set  to 
work.  The  pulley  G  is  driven  by  a  belt  from  a  steam-engine,  and 
works  the  pump  A  F.  This  forces  oil,  under  great  pressure,  through 
the  small  tube  B,  into  the  rear  of  the  cylinder  H,  thus  driving  out  the 
large  piston  P  with  a  total  pressure  equal  to  the  area  of  its  section  mul- 


HYDRAULIC  COTTON-PRESS. 


191 


tiplied  into  the  intensity  of  the  oil-pressure  as  indicated  by  a  gauge. 
Machines  of  this  sort  are  in  use  which  can  produce  pressures  of  200 
tons.  They  are  employed,  as  well,  for  forcing  the  great  driving-wheels 
of  locomotives  on  to  their  axles. 
In  Fig.  94  is  shown  another 
form  of  hydraulic  press,  used 
for  compressing  the  loose  cot- 
ton, as  it  comes  from  the  fields, 
into  bales  for  transportation. 
The  cotton  is  fed  in  at  A,  near 
the  top.  When  the  tall  receiver 
is  full,  the  piston,  just  fitting 
the  receiver,  and  seen  through 
the  opening  in  its  lower  part,  is 
forced  up,  thus  greatly  reduc- 
ing the  bulk  of  the  loose  cot- 
ton. This  piston  is  the  upward 
extension  of  the  piston  of  a 
hydraulic  press  located  below 
in  the  brick  well.  The  pipe  B 
conveys  the  oil,  under  pressure, 
from  the  pump  to  the  press. 

That  the  Pressure 
due  to  a  Column  of 
Liquid  depends  on  the 
Depth  and  not  on  the 
amount  of  liquid  in  the  column,  may  be  illustrated  by  such 
an  experiment  as  this  : 

EXPERIMENT. — Into  a  water-tight  cask  fasten  a  small  tube  (of  glass 
or  eighth-inch  gas-pipe,  or  even  a  thick-walled  small  rubber  tube)  rising 
to  a  height  of  10  feet  or  more  above  the  cask.  Fill  the  cask  with  water, 
and  then  pour  water  into  the  tube.  Although  the  cask  is  very  strong, 
it  will  be  burst  by  the  internal  pressure  when  the  water-column  is  only 
a  few  feet  high.  Of  course,  the  weight  of  the  water  in  the  column 
would  be  entirely  insufficient  for  this.  But  the  pressure  on  every 
square  inch  of  the  interior  of  the  cask  is  that  due  to  a  water-column 
of  this  height,  and  it  depends  only  on  the  height,  and  not  at  all  on  the 
size  or  shape  of  the  column. 

Similar  effects  may  be  produced  in  nature,  as  in  the  case  of  a 
mass  of  rock  through  which  runs  a  long  crevice,  communicating  with 


FIG.  94.— HYDRAULIC  COTTON-PRESS. 


192  LIQUIDS   AND   GASES. 

a  large  cavity  below,  full  of  water,  and  having  no  outlet.  When  a 
shower  fills  the  crevice,  so  great  a  pressure  may  be  generated  as  to  rend 
the  rock  in  fragments.  Draw  a  diagram  illustrating  this. 

QUESTIONS.— State  the  hydrostatic  law  of  the  transmission  of  pressure.  Describe 
the  experiment  illustrating  it.  How  is  liquid  pressure  and  its  transmission  ex- 
plained on  the  molecular  hypothesis  ?  What  is  meant  by  the  intensity  of  liquid 
pressure  ?  By  total  pressure  ?  In  a  large,  closed  vessel,  full  of  water,  a  pressure 
is  exerted  on  a  square  inch,  at  one  point,  of  10  pounds  ;  what  will  be  the  pressure 
on  a  surface  of  a  square  foot  anywhere  else  in  the  vessel,  neglecting  the  weight 
of  the  liquid  ?  Suppose  a  tank  to  be  full  of  water  ;  is  the  intensity  of  the  out- 
ward pressure  on  the  side  of  the  tank  the  same  for  all  points  in  a  horizontal 
line  ?  In  a  vertical  line  ?  Why  ? 

According  to  what  law  does  the  intensity  of  the  pressure  increase  with  the  depth  ? 
Illustrate  by  the  tumblerful  of  shot.  Give  the  rules  for  finding  the  intensity 
of  water-pressure  at  any  depth.  For  finding  the  average  intensity  of  pressure 
upon  a  given  surface.  For  finding  the  total  pressure  on  that  surface.  If  the 
liquid  be  something  other  than  water,  how  are  these  rules  changed  ? 

What  would  be  the  intensity  of  the  pressure  at  a  depth  of  1,000  feet  in  fresh  water  j 
In  salt  water  of  a  density  of  1  '03  ?  What  would  be  the  total  pressure,  there,  on 
the  top  of  a  box  2  by  4  feet  ? 

Show  by  experiment  that  in  a  mass  of  water  there  is  upward  as  well  as  downward 
pressure.  Show  that  there  is  pressure  in  all  directions.  Why  does  the  surface 
of  water  assume  a  "  level"  ?  Is  the  surface  of  water  at  rest  truly  plane  ?  If 
not,  what  is  its  shape  ?  No  matter  what  the  size  or  shape  of  a  body  of  water 
may  be,  its  surface  has  the  same  level  throughout— that  is,  it  is  equally  distant 
at  every  point  from  the  earth's  center.  Accordingly,  the  surface  of  the  ocean 
is  spherical ,'  and  this  ive  know  to  be  the  case  from  always  seeing  the  mast  of  a 
vessel  approaching  in  the  distance  before  we  see  the  hull.  The  convexity  is  so 
slight,  however,  that  in  small  bodies  of  liquid  the  curvature  is  imperceptible, 
and  we  may  consider  their  surfaces  as  perfectly  flat.  Show  why  water  in 
communicating  vessels  stands  at  the  same  level.  Would  this  be  true  for  ves- 
sels of  unequal  sizes,  but  so  small  that  capillarity  affects  them  ?  Describe  the 
principle  and  use  of  the  Spirit-level. 

Explain  the  principle  of  the  Hydraulic  press.  If  the  large  piston's  area  is  200  inches 
and  that  of  the  small  one  045  inch,  how  much  is  the  pressure  on  the  large 
piston  for  1  pound  on  the  small  one  ?  Suppose  the  small  piston  is  worked  by  a 
lever  of  the  second  order,  with  a  leverage  of  10,  and  a  power  of  100  pounds  is 
applied  at  the  lever  end,  what  will  be  the  lifting  force  on  the  large  piston,  neg- 
lecting friction,  etc.  Suppose  the  press  worked  thus  by  a  man,  how  much 
gain  of  work  is  there  over  what  the  man  can  do  ?  What  is  the  kind  of  advan- 
tage gained  by  using  the  press  ?  How  much  is  the  gain  ?  Deduce  the  law  of 
action  of  the  press  by  applying  the  principle  of  the  conservation  of  energy.  By 
means  of  the  law  of  hydrostatic  pressure.  What  are  some  of  the  practical  ap- 
plications of  the  press  ?  Describe  the  wheel-press  ;  the  cotton-press.  Explain 
the  experiment  of  bursting  a  cask  by  a  small  weight  of  water.  What  similar 
effect  is  produced  in  nature  ? 


PRINCIPLE   OF  ARCHIMEDES. 


193 


BUOYANCY  OF  LIQUIDS.— SPECIFIC  GRAVITY. 

A  Body  submerged  in  a  Liquid  appears  to  lose  a  part 
of  its  weight,  the  amount  lost  being  equivalent  to  the  weight 
of  an  equal  bulk  of  the  liquid.  This  is  called,  from  its  dis- 
coverer, the  Principle  of  Archimedes. 

EXPERIMENT. — Tie  a  string  to  a  stone.  Hold  the  end  of  the  string 
in  your  hand  and  lower  the  stone  into  water.  Notice  that  when  the 
stone  begins  to  enter  the  water  it  appears  lighter 
in  weight,  and  that  it  continues  to  lose  weight 
more  and  more  as  you  lower  it  until  it  is  all  im- 
mersed. It  then  appears  of  the  same  weight, 
whether  just  under  the  surface  or  at  any  greater 
depth.  Instead  of  a  string  use  a  rubber  band,  and 
notice  how  it  shortens  as  the  stone  goes  under 
water ;  or,  better  still,  attach  the  stone  to  a  spring- 
balance.  A  stone  so  heavy  that  you  can  hardly 
lift  it  in  the  air  can  be  easily  moved  under  water, 
for  its  apparent  weight  will  be  only  half  or  two 
thirds  as  much  as  its  real  weight. 

When  under  water,  the  body  must,  of 
course,  thrust  aside,  or  displace,  a  volume 
of  water  equal  to  its  own  bulk  in  order  to 
make  room  for  itself.  The  apparent  loss  of 
weight  is  equal  to  the  weight  of  water  dis- 
placed. This  may  be  experimentally  shown 
as  follows : 


FIG.  95.— PRINCIPLE 
OF  ARCHIMEDES. 


Let  A  (Fig.  95)  be  a  tin  vessel  open  at  the  top,  and  B  another 
which  exactly  fills  A  but  which  has  a  water-tight  top  soldered  upon 
it  and  lead  enough  inside  to  make  it  sink.  Hang  them  upon  a  spring- 
or  equal-arm  balance  and  read  the  balance.  Then  lower  B  into  water 
until  it  is  wholly  submerged,  so  that  the  water  surface  is  at  C  D.  The 
balance  will  read  less,  showing  that  B  has  apparently  lost  weight. 
Pour  water  into  A  until  it  is  just  full.  You  will  have  added  a  volume 
and  weight  of  water  exactly  equal  to  that  displaced  by  B.  The  bal- 
ance will  be  found  to  read  the  same  as  before  B  was  immersed.  Hence 
the  apparent  loss  of  weight  of  B  is  just  equal  to  that  of  its  own  volume 
of  water.  The  same  experiment  may  be  tried  with  any  other  liquid. 


X94  LIQUIDS  AND  GASES. 

This  loss  of  weight  is  apparent,  not  real.  The  cause  of 
the  difference  is  not  that  the  attraction  between  B  and  the 
earth  is  lessened,  but  that  B  is  pushed  upward  by  another 
force  which  partly  counterbalances  its  weight.  This  lifting 
force  is  due  to  the  pressure  of  the  liquid,  and  is  called  the 
Buoyancy  of  the  liquid.  The  downward  pressure  of  the 
liquid  on  the  top  of  B  is  that  corresponding  to  its  depth. 
The  upward  pressure  on  the  bottom  is  that  corresponding 
to  its  greater  depth,  and  is  therefore  greater  than  the  down- 
ward pressure,  so  that  the  resultant  pressure  is  upward. 

Suppose  the  body  were  a  cube  in  water  with  its  sides  vertical.  The 
downward  pressure  on  the  top  would  be  62'5  x  area  x  depth  of  top. 
The  upward  pressure  on  the  bottom  would  be  62*5  x  area  x  depth  of 

bottom  ;  but  area  of  top  =  area  of  bot- 
tom, and  the  depth  of  bottom  is  greater 
than  that  of  the  top  by  the  length  of 
the  side.  Hence  pressure  on  bottom— 
pressure  on  top  =•  62-5  x  area  x  length 
of  side.  But  area  x  length  of  side  = 
volume  of  cube,  and  therefore  62*5  x 
:  area  x  length  =  weight  of  water  equal 
in  volume  to  the  cube.  The  buoyancy 
is  then  equal  to  the  weight  of  an  equal 

volume  of  water.     It  is  obvious  that 
FIG.  96.— IMMERSED  CUBE. 

the  buoyancy  will  not  vary  with  the 

depth,  since  it  depends  only  on  the  difference  of  depth  of  the  top  and 
the  bottom  of  the  cube,  which  is  always  the  same,  and  on  the  weight 
of  a  cubic  foot  of  water  which  changes  but  slightly  with  the  distance 
below  the  surface.  Liquids  denser  than  water  will  produce  a  greater, 
those  less  dense  a  less,  buoyancy.  For  such,  instead  of  62'5  we  must 
write  their  weight  per  cubic  foot.  A  similar  proof  holds  for  bodies  of 
any  form,  since  they  may  be  regarded  as  made  up  of  a  large  number 
of  very  minute  cubes,  to  each  of  which  this  demonstration  will  apply. 

Floating  Bodies. — If  a  body  floats  when  put  into  wa- 
ter, it  displaces  a  weight  of  water  just  equal  to  its  own 
weight.  Place  any  substance,  for  example,  a  piece  of  wood, 
in  water ;  you  will  see  that  part  of  it  is  beneath  and  part 
above  the  surface.  In  order  that  it  may  float,  the  body  must 


FLOATING  BODIES.  195 

be  buoyed  up  by  a  force  equal  to  its  weight.  But  the  buoy- 
ancy is  equal  to  the  weight  of  the  water  displaced  by  the 
immersed  portion,  as  shown  above.  Hence,  when  floating, 
a  body  must  be  displacing  a  weight  of  water  exactly  equal 
to  its  own  weight. 

Any  solid  or  liquid  less  dense  than  water— e.  g.,  oil — if  entirely  im- 
mersed in  water  will  be  buoyed  up  by  a  force  greater  than  its  own 
weight.  Why  f  It  will  therefore  tend  to  rise  through  the  water  and 
float  on  top.  Warm  water  is  less  dense  than  cold  water,  therefore  it 
will  tend  to  rise  in  currents  through  the  cold  water.  In  a  glass  vessel 
heated  at  the  bottom,  you  can  see  these  currents.  Cream  is  less  dense 
than  milk,  and  therefore  rises.  It  is  to  be  noted  that  we  speak  of 
these  things  as  rising,  although  they  really  do  not  rise  of  themselves 
but  are  forced  upward  by  the  upward  pressure  due  to  the  excess  of 
weight  of  the  heavier  liquid  surrounding  them. 

With  the  lungs  full  of  water  or  entirely  empty  of  air,  the  human 
body  is  probably  slightly  denser  than  water.  When  the  lungs  are 
full  of  air,  it  is  less  dense  than  water,  so  that  it  will  rise  to  the  surface 
without  effort  on  the  part  of  a  swimmer.  But  the  head  is  more  dense 
than  other  parts,  so  that  some  slight  effort  is  generally  necessary 
to  keep  the  head  at  the  surface.  In  swimming  in  the  usual  position, 
more  of  the  head  is  kept  out  of  water  than  the  buoyancy  can  sustain. 
Hence,  effort  is  necessary  for  this  purpose  as  well  as  for  propulsion. 
In  floating  on  the  back  with  barely  just  enough  of  the  face  out  for 
breathing,  no  effort  is  required  except  a  very  slight  one  with  the  hands 
to  preserve  the  proper  position  of  the  body.  The  knowledge  of  how  to 
float  thus  upon  the  back  with  very  little  effort  and  to  breathe  when 
the  head  is  in  the  troughs  between  waves,  might  save  many  lives  in 
accidents  on  the  water.  Notice  some  time,  when  bathing  in  shallow 
water,  how  light  the  body  appears  if  wholly  immersed,  and  how  fast  it 
seems  to  grow  heavy  as  you  rise  out  of  the  water  to  a  standing  posture. 
This  will  easily  convince  you  of  the  great  waste  of  effort  you  would 
make  in  swimming  or  floating  if  you  were  to  try  to  keep  out  of  water 
more  than  just  enough  of  the  face  to  enable  you  to  breathe. 

Density,  or  Specific  Gravity. — Application  of  the 
Principle  of  Archimedes  is  made  to  determine  the  relative 
densities  of  bodies.  Density  is  the  mass  per  unit  volume. 
In  scientific  work,  the  density  is  expressed  in  grammes  per 
cubic  centimetre ;  that  of  water  is  almost  exactly  one  gramme 


196 


LIQUIDS  AND  GASES. 


per  cubic  centimetre.  In  engineering  and  commercial  worK, 
densities  are  not  usually  stated  in  units  of  mass,  but  the 
density  is  given  relatively  to  that  of  water  taken  as  a 
standard.  This  relative  density  is  called  Specific  Gravity ; 
it  is  more  properly  Specific  Density,  or  merely  Density. 
By  specific  gravity,  then,  is  meant  the  ratio  of  the  mass  of 
any  volume  of  the  given  substance  to  the  mass  of  an  equal 
volume  of  pure  water  at  a  standard  temperature.  As  the 
mass  of  a  cubic  centimetre  of  water  is  1  gramme,  the  spe- 
cific gravity  of  a  substance  referred  to  water,  and  its  density 
in  grammes  per  cubic  centimetre,  are  numerically  the  same. 
Methods  of  measuring-  Specific  Gravity — Weigh 
the  body  whose  specific  gravity  is  to  be  determined  in  air, 
and  then  when  hung  in  water,  as  in  Fig. 
97.  The  difference  in  weight  will  be  the 
loss  of  weight  in  water,  which  is  the  weight 
of  an  equal  bulk  of  water.  Divide  the 
weight  in  air  by  the  loss  of  weight  in  water. 
The  quotient  will  be  the  specific  gravity. 

To  find  the  specific  gravity  of  a 
liquid,  like  a  solution  of  salt,  weigh  a 
glass  -  stoppered  bottle  when  empty 
and  dry,  again  when  completely  filled 
with  the  liquid,  and  a  third  time  when 
Subtracting  the  weight  of  the  bottle  when 
empty  from  each  of  the  other  weights,  will  give  the 
weights  of  equal  volumes  of  the  liquid  and  of  water. 
The  quotient  of  the  first  by  the  second  will  be  the  specific 
gravity  desired.  A  similar  method  with  the  bottle  may 
be  used  for  solids. 

The  Hydrometer. — The  specific  gravities 
of  liquids  are  also  determined  readily,  when  very 
great  accuracy  is  not  required,  by  means  of  the 
Hydrom'eter,  one  form  of  which  is  shown  in 
Fig.  98. 

A  hollow  glass  bulb  is  weighted  slightly  with  shot  or  mercury  at 
the  lower  end,  D,  and  is  prolonged  upward  into  a  thin  tube,  A.     In- 


Fio.  97. 
full  of  water. 


SPECIFIC  GRAVITY. 

side  of  this  tube  is  a  paper  scale,  A  B.  When  the  hydrometer  is  im- 
mersed in  water,  as  shown  in  the  figure,  it  settles  to  such  a  depth 
that  the  reading  on  the  scale  at  the  water  surface  B  is  1.  If  it  is  im- 
mersed in  a  less  dense  liquid,  it  will  sink  deeper,  and  the  reading  at 
the  liquid  surface  will  give  the  specific  gravity  of  the  liquid  referred 
to  water.  If  it  is  immersed  in  a  liquid  denser  than  water,  it  will  sink 
less  deep,  and  the  reading  will  again  give  the  specific  gravity  of  the 
liquid.  Certain  hydrometers  are  graduated  to  give  specific  gravities 
directly ;  some,  with  an  arbitrary  scale ;  and  others,  for  special  pur- 
poses, such  as  testing  milk,  showing  the  strength  of  an  alcoholic  mixt- 
ure, etc.  The  depth  to  which  the  hydrometer  will  sink  in  the  pure 
article  being  known,  any  different  result,  when  a  liquid  is  tested,  indi- 
cates adulteration. 

TABLE   OF   DENSITIES   OR   SPECIFIC   GRAVITIES. 

Platinum 22'0  Water     ,v     >;      ,     •  .;    -  r  l-OO 

Gold .        .        .        .        .        .        .  19'4  Olive-oil    .        .       .       .  ~    .  0'92 

Mercury  .        .        .        .        .        .  13'6  Average  density  of  human 

Lead 11'4  body    .        .        .        .        .  0'89 

Silver 10'5  Alcohol  (absolute)  .        .        .  0'79 

Brass 8'4  Wood  (pine)     ....       .  0'66 

Iron  .        .        .....       .  7'5       Cork 0'24 

Average  density  of  the  earth       .  5'67  Air     .        .        .        .        .       .  0'0012 

Marble     .        .        .       .       *    .   .  2'8  Hydrogen         .        ."     '.        .  0-000083 

Flow7  of  Water. — Let  A  B  (Fig.  99)  be  any  reservoir 
of  water  kept  at  a  constant  level  A.  Suppose  a  pipe  to  lead 
from  it  at  0  along  to  D  E  F  G  L.  Let  D  Hy  E  I,  etc.,  be 
open  vertical  glass  tubes.  At  first  suppose  D  L  to  be  a 
straight  uniform  horizontal  pipe.  Now,  if  this  is  closed  at 
L,  the  water  will  flow  out  of  C  until  the  pipes  D  H,  E  I, 
etc.,  are  all  filled  up  to  the  level  H  IJ  K,  which  is  the  same 
as  A.  But  if  L  is  opened,  the  water  in  the  glass  pipes  will 
drop  to  some  such  points  as  H',  I',  J',  K',  although  A  re- 
mains the  same.  Why  ?  The  heights  of  liquid  D  H',  etc., 
are  supported  by,  and  thus  measure,  the  pressures  in  D  L 
at  the  points  D,  E,  F,  G.  When  there  is  no  flow,  the  liquid 
is  at  rest,  the  pressure  must  be  the  same  throughout  D  L, 
and  the  heights  D  H,  E  I,  etc.,  must  all  be  the  same.  When 
the  water  is  flowing  out  at  L,  it  has  to  overcome  friction  on 
the  sides  of  the  tube  and  upon  itself. 


198 


LIQUIDS  AND  GASES. 


H 
H' 

1 

J 

K 

l' 

j' 

K'     L 

FIG. 


D  E  F  G 

.—FLOW  OP  WATER  THROUGH  PIPES. 


If  any  of  the  vertical  pipes  were  removed  from  the  pipe  D  L,  the 
water  would  issue  from  the  opening  as  a  jet  or  fountain,  which  would 
rise  as  high  as  the  water  formerly  stood  in  the  pipe.  For  instance,  if 
E  I  were  removed,  the  fountain  at  the  point  would  rise  to  the  height 
I  if  L  were  closed,  or  to  I'  if  L  were  open.  This  statement,  however, 

needs     modifica- 

IA  SU         i          .IK  tion;  for  the  jet 

would  meet  with 
some  air  resist- 
ance which  would 
reduce  its  rise, 
and  the  extra  rate 
of  flow  through 

the  pipe  C  D  E  required  to  supply  the  quantity  escaping  at  E,  and  also 
the  friction  of  the  orifice,  would  somewhat  reduce  the  pressure,  and 
hence  the  height  of  the  fountain. 

At  L  the  pressure  is  only  such  as  to  give  the  water  the  energy 
which  it  acquires  on  leaving  L.  At  G  the  pressure  must  be  greater 
than  at  L  by  an  amount  necessary  to  do  the  work  of  driving  the  water 
through  G  L  against  the  friction.  At  F  it  must  be  greater  still  by  the 
amount  necessary  for  the  work  in  F  G,  and  so  on  back  to  the  source  C. 
The  resistance  to  flow  through  pipes  is  due  partly  to  friction,  partly 
to  other  causes ;  it  increases  with  increase  in  length  of  pipe,  rough- 
ness of  interior,  number  of  joints,  number  of  bends  or  turns,  angle  of 
bends,  number  of  irregular  enlargements  or  contractions  of  pipe,  and 
rate  of  flow.  It  diminishes  with  increase  of  diameter  of  pipe  propor- 
tionally to  about  the  fourth  power  of  the  diameter.  Similar  statements 
apply  to  the  flow  of  gases  through  pipes,  as  in  ventilating  apparatus. 
These  laws  find  very  important  practical  application  in  water-supply 
and  sewerage  systems,  in  heating  and  ventilating  apparatus,  in  steam 
piping,  and  in  hydraulic  work  generally. 

Water  in  the  Soil. — Water  is  also  continually  flowing 
through  the  soil,  in  some  places  along  regular  underground 
channels,  but  more  generally  in  a  steady  flow  or  percolation. 
Fig.  100  may  serve  to  give  some  idea  of  this.  Let  A  B  C  D 
represent  the  surface  of  the  ground  shown  in  a  vertical  sec- 
tion, and  suppose  the  soil  to  be  a  uniform  gravel  or  sand, 
sloping  off  to  a  lake  at  D  E.  Then  the  soil  would  be  gen- 
erally found  to  be  filled  with  water  below  a  certain  depth 
indicated  by  the  shading  below  F  G  H  I  D.  This  water 


FLOW  OF   WATER.  199 

surface  would  be  somewhat  definitely  marked,  but,  of  course, 
not  perfectly  sharp,  as  the  soil  above  it  would  be  damp. 
The  water  below  it  would  be  continually  flowing  in  a  mass 
toward  the  lower  level,  but  the  flow  would  be  quite  slow, 
owing  to  the  resistance  to  flow  through  the  soil.  The  source 
of  this  water  is  the  rain  falling  upon  and  soaking  into  the 
soil,  and  the  surface  F  G  I  is  lower  after  dry  and  higher 
after  rainy  times.  Most  soils  are  not  uniform,  but  contain 
ledges,  or  strata  of  clay,  sand,  or  gravel.  These  strata  greatly 
modify  the  actual  distribution  of  water.  Artesian  wells,  in- 
termittent springs,  etc.,  owe  their  action  to  such  peculiari- 
ties of  soil  formation. 

If  at  any  point 
H  the  ground 
shows  a  natural  de- 
pression below  the 
surf  ace  FG1,  there 
will  be  a  Spring 
or  a  standing  pool 
at  that  point.  If  FIG.  lOO.-FLow  OP  WATER  IN  THE  SOIL. 

a  hole  be  dug,  as 

at  B  W,  until  it  is  below  the  water  surface,  it  will  contain  water  up  to 
that  surface,  forming  a  Well.  If  the  well  is  so  deep  that  the  ground- 
water  surface  is  never  below  its  bottom,  the  well  will  never  be  dry. 

QUESTIONS. — What  is  meant  by  the  buoyancy  of  a  liquid  ?  How  much  does  a 
body  immersed  in  water  appear  to  lose  in  weight  ?  How  much  would  it  appear 
to  lose  in  mercury  ?  In  any  other  liquid  ?  In  any  other  fluid  ?  Show  this  by 
experiment.  Describe  an  experiment  to  prove  the  principle  of  Archimedes. 
Prove  the  principle  for  a  cube  immersed  in  water  by  means  of  the  law  of  hydro- 
static pressure.  Prove  it  for  a  body  of  any  form  whatever.  Why  does  a  piece 
of  wood  tend  to  rise  when  wholly  immersed  in  water  ?  With  how  much  force  ? 

What  enables  some  objects  to  float  ?  How  much  liquid  does  a  floating  object  dis- 
place ?  Why  will  iron  float  on  mercury  but  sink  in  water  ?  Why  will  oil  float 
on  water  but  sink  in  alcohol  ?  About  three  quarters  of  the  mass  of  the  human 
body  is  water  ;  of  the  remaining  parts  much  is  more  dense  than  water.  How, 
then,  is  it  possible  that  the  body,  on  the  whole,  is  less  dense  than  water  ?  If  a 
person  is  about  to  dive  and  wishes  to  return  as  quickly  as  possible  to  the  sur- 
face, why  should  he  thoroughly  inflate  his  lungs  ?  How  does  your  experience 
in  rising  out  of  water  illustrate  the  buoyancy  of  liquids  ? 

Define  Density  ;  Specific  Gravity.  Why  are  the  density  in  grammes  per  cubic 
centimetre  and  the  specific  gravity  referred  to  water  numerically  the  same  ? 
What  is  the  density  of  gold  ?  Of  water  ?  Of  air  ?  Describe  a  method  for  find- 


200  LIQUIDS  AND  GASES. 

ing  the  specific  gravity  of  a  solid  ;  of  a  liquid.  Given  a  block  of  iron  1  inch 
long,  2  inches  wide,  and  3  inches  high;  how  could  you  find  its  density  without 
immersing  it  in  water  or  wetting  it  ?  How  should  you  suppose  the  density  of  a 
gas  might  be  determined  ?  A  piece  of  unknown  material  whose  weight  is  23'25 
grammes  is  found  to  weigh  20  "15  grammes  in  water.  What  is  its  specific  grav- 
ity ?  What  is  its  density  ?  Refer  to  the  table  on  page  197  and  see  what  the  sub- 
stance probably  is. 

What  is  the  weight  of  a  cubic  foot  of  water  ?  Of  iron  ?  of  air  ?  What  is  the 
volume  in  cubic  feet  of  a  ton  of  water  ?  Of  a  ton  of  iron  ?  Describe  the  flow 
of  water  through  pipes  by  means  of  Fig.  99  (page  198).  What  factors  affect 
the  resistance  of  pipes  to  the  flow  of  liquids  ?  Why  is  a  pipe  of  twice  the  area 
of  section  more  than  twice  as  good  ?  Why  is  a  straight  pipe  better  than  a 
crooked  one  ?  A  short  one  than  a  long  one  ?  A  large  one  than  a  small  one  ? 
One  with  a  smooth  interior  than  one  with  a  rough  interior  ?  One  with  few 
joints  and  turns  than  one  with  many  ?  Do  these  statements  apply  also  to  chim- 
ney-flues ?  To  ventilating  flues  ?  Would  a  chimney  u  draw  "  well  out  of  a  room 
into  which  no  air  could  enter  ?  Where  do  you  suppose  the  air  enters  a  room 
when  all  the  doors  and  windows  are  closed  ? 

Describe  the  simplest  case  of  the  distribution  and  flow  of  water  in  a  uniform 
sand-hill.  If  in  Fig.  100  there  were  a  horizontal  layer  of  clay  across  the  hill 
one  quarter  way  up  from  the  lake,  where  should  you  expect  to  find  springs  ? 


GASES  AND   THEIR  PROPERTIES. 

Gases  have  Weight. — We  easily  perceive  the  weight 
of  most  solids  and  liquids  because  they  weigh  more  than  the 
air  displaced.  You  will  see,  however,  on  reflection,  that  we 
can  not  weigh  water  in  water,  as  the  quantity  to  be  weighed 
would  be  buoyed  up  by  a  force  equal  to  its  own  weight.  For 
a  similar  reason  we  are  not  sensible  that  air  has  weight,  for 
we  ordinarily  weigh  bodies  in  air,  and 
air  weighed  in  air  would  appear  without 
weight ;  try  the  following 

EXPERIMENT.— Hang  the  hollow  globe  of 
Pig.  101  on  one  arm  of  some  moderately  sensi- 
tive balance,  and  counterpoise  it  by  sand  or  any 
weights  in  the  other  pan.  Then  take  off  the 
globe  and  exhaust  the  air  with  the  air-pump  or 
by  sucking  it  out  with  the  mouth.  Close  the 
FIG.  101.  stop-cock  and  again  hang  the  globe  on  the 

balance,  the  same  weight  remaining  in  the  other 

pan.     The  balance  will  now  tip,  showing  the  globe  to  be  much  lighter. 

Why  f    Nothing  has  been  changed  except  that  air  has  been  taken  out 


ATMOSPHERIC   PRESSURE. 


201 


The  weight^  is  less.    Therefore  the  air  removed  must 
In  a  similar  manner,  other  gases  may  be  shown  to  have 


of  the  globe. 
have  weight. 
weight. 

A  litre  of  air  weighs  only  1*2  grammes  at  ordinary  temperatures 
and  pressures,  while  a  litre  of  water  weighs  1,000  grammes,  so  that  the 
density  of  air  is  only  about  ^,  or  roughly  -nf^,  of  that  of  water. 


Atmospheric  Pressure. — The  earth  is  surrounded  on 
all  sides  by  a  layer  of  air  several  miles  deep  called  the  At- 
mosphere. As  this  air  has  weight,  it  must  press  down  upon 
the  earth's  surface  and  everything  on  the  earth  just  as  the 
water  does  on  the  .ocean-bottom  and  on  all  submerged  ob- 
jects. At  sea-level,  the  pressure  of  the  air  is  in  all  directions 
about  15  pounds  to  the  square  inch.  We  may  show  the 
existence  of  such  pressure  by  several  experiments. 

EXPERIMENTS. — Fig.  102  illustrates  the  "  Magdeburg 
Hemispheres " — hollow  metal  hemispheres,  with  their 
edges  carefully  ground  and  greased.  Put  them  together 
and  you  can  pull  them  apart  easily,  whether  the  cock 
is  open  or  closed  ;  but  put  them  together  and  exhaust 
the  air  partly  from  within  them  (by  air-pump  or  mouth) 
and  close  the  cock.  You  will  then  find  it  very  difficult 
to  pull  them  apart  in  any  direction.  Why  I  Because 
the  atmosphere,  owing  to  the  pressure  produced  by  its 
weight,  is  forcing  them  together  on  all  sides. 

Over  the  top  of  a  glass  vessel  like  that  shown  in 
Fig.  103,  stretch  a  piece  of  thin  sheet  rubber.  Place 
the  glass  upon  the  plate  of  the  air-pump.  The  rubber 

will  be  flat.  Exhaust  some  of  the  air. 
The  rubber  will  begin  to  bulge  inward. 
Why  ?  Because  the  atmosphere  presses 
down  upon  it.  But  this  was  also  the  case 
before  the  air  was  removed  ;  why  did  the 
bulging  not  occur  then?  Because  the 
pressure  was  balanced  by  the  upward  press- 
ure of  the  air  beneath.  Instead  of  the  glass 
shown,  a  lamp  -  chimney,  with  a  rubber 
stopper  in  one  end  and  the  sheet  rubber 

over  the  other,  may  be  used.    The  air  may  then  be  removed  by  sucking 
with  the  mouth  upon  a  glass  tube  passing  through  the  stopper.    The 
14 


FIG.  IOB.-TO  ILUSTRATE  AT- 
MOSPHERIC  PRESSURE. 


202 


LIQUIDS  AND  GASES. 


FIG.  104.— ILLUSTRATING 
DOWNWARD  ATMOS- 
PHERIC PRESSURE. 


same  result  will  be  reached  if  the  rubber  surface  is  downward,  side- 
wise,  or  in  any  position,  showing  that  the  atmospheric  pressure  is 
exerted  in  all  directions.  If  the  palm  of  the 
hand  is  put  in  place  of  the  rubber  sheet,  it 
becomes  bulged  inward  when  the  pressure  is 
removed  from  beneath  it. 

Place  a  thin  green  leaf  over  the  lips  and 
draw  in  the  breath  strongly.  The  leaf  will 
break  in  with  a  snap.  Why  1 

Over  the  top  of  an  argand  chimney,  or 
any  other  glass  tube,  tie  a  bit  of  thin  sheet 
rubber.  Place  the  whole  sidewise  under  water 
and  fill  it.  Then  invert  it  as  shown  in  Pig. 
104.  The  rubber  is  drawn  in  more  and  more 
the  higher  it  is  above  the  water  outside  the 
tube.  When  the  rubber  is  level  with  the  water  outside,  it  is  flat. 
Why  f  Because  the  water  column  below  the  rubber  transmits 
the  atmospheric  pressure  to  the  under  side  of  the  rubber,  and 
the  upward  and  downward  pressures  are  equal.  But  as  the 
tube  is  raised,  the  water  column  itself  balances  part  of  the 
atmospheric  pressure,  so  that  the  upward  pressure  on  the 
under  surface  of  the  rubber  is  less  than  the  downward  press- 
ure on  the  top. 

Put  a  tumbler  under  water  and  fill  it.     Then  draw  it  out 
bottom  upward.    Notice  what  happens  and  give  the  reason 
for  it.    Does  the  tumbler  feel  heavier  f    Why  ?    How  much  ? 
A  glass  tube  A  B  (Fig.  105)  is  closed  at  both  ends  by 
stoppers.    Through  the  lower  stopper  passes  a  small  tube  D  C 
drawn  out  to  a  fine  open  point  at  C.    Suck  out  as  much  of  FIG.  105. 
the  air  by  the  mouth  at  D  as  you  can.    Then  close  D  with  the 
finger,  thrust  the  lower  part  of  the  apparatus  under  water,  and  observe 
what  occurs.     Explain  the  action.* 

The  Barometer. — Melt  together  in  the  gas-flame  the 
end  of  a  clean,  dry,  glass  tube,  three  feet  long  and  one  eighth 
to  one  fourth  inch  inside  diameter.  Fill  it  with  mercury. 
Bubbles  of  air  will  adhere  all  along  the  inside  of  the  tube. 
To  get  rid  of  these,  leave  a  quarter  of  an  inch  of  the  tube  at 
the  open  end  empty.  Put  the  finger  over  this  end  and  turn 


*  This  and  some  other  simple  apparatus  will  be  found  described  in  Hopkins1* 
Experimental  Science,  Munn  &  Co.,  New  York. 


THE  BAROMETER, 


203 


the  tube  into  a  nearly  horizontal  position,  but  with  the 
closed  end  a  little  higher.  The  large  bubble  will  run  up- 
ward slowly  toward  the  closed  end,  collecting  the  smaller 
ones  on  its  way.  Then  raise  the  open  end,  and  the  bubble 
will  run  back.  Repeat  this  operation  several  times,  until 
most  of  the  bubbles  are  removed.  Next  fill  the  remaining 
space  with  mercury,  put  the  finger  over  the  open  end,  and 
invert  the  tube  into  the  position  shown 
in  Fig.  106,  where  B  is  the  closed  end  R  F 

and  A  is  a  dish  of  mercury.     Such  a  tube 
is  called  a  Barometer. 

The  mercury  in  the  barometer  will  fall  at 
once  to  some  point  C.  Measure  the  height  A  C 
from  the  surface  in  the  dish.  It  will  be  found  to  be, 
on  the  average,  at  the  sea-level,  about  30  inches 
(from  28  to  31,  according  to  the  condition  of  the 
weather).  This  experiment  is  called,  from  its  dis- 
coverer, Torricelli,  the  Torricellian  experiment. 

Repeat  with  a  different  tube,  and  A  C  will  be 
found  the  same,  except  for  variations  due  to  im- 
perfect removal  of  air,  capillarity,  etc. 

Why  does  the  mercury  not  fall  to  A  ?  Use 
a  much  longer  tube ;  A  C  will  be  the  same.  Use 
a  tube  less  than  A  C  in  length,  and  the  mercury 
will  remain  up  to  the  top.  Compare  this  with  the 
experiment  of  Fig.  103,  and  with  the  tumbler  ex- 
periment (page  202).  The  atmospheric  pressure, 
then,  is  transmitted  through  the  mercury  in  the 
dish  to  the  bottom  of  the  tube,  and  there  presses 
upward  with  a  force  sufficient  to  balance  the 
downward  pressure  of  a  column  of  mercury  of  a 
height  A  C— about  30  inches.  The  barometer, 
therefore,  measures  the  atmospheric  pressure,  and 
hence  its  name  (weight-measurer).  This  pressure 
at  sea-level  (see  example,  page  186)  is  about  14-7 
pounds  on  each  square  inch  of  surface. 

If  the  atmospheric  pressure  will  balance  a  column  of  mercury  30 
inches  high,  it  will  sustain  a  water  column  of  34  feet,  for  these  two 
columns  produce  equal  pressure  (see  example,  page  186).  To  balance 


H 

FIG.  106.— FORMS  OF 
BAROMETER. 


204  LIQUIDS  AND  GASES. 

the  atmospheric  pressure  by  a  water-column,  we  should  need  a  tube  at 
least  34  feet  instead  of  30  inches  long. 

If,  instead  of  a  straight  tube  inverted  in  a  dish  of  mer- 
cury, a  tube  be  bent  into  the  second  form  shown  in  Fig.  106, 
the  end  F  being  closed  and  the  short  end  open,  the  mercury 
will  stand  with  a  difference  of  level  E  D,  equal  to  A  C  of 
the  other  tube. 

The  space  above  the  mercury  in  B  C  and  F  D  is  called 
a  vacuum  (empty  space).  If  the  experiment  were  perfectly 
performed,  it  would  contain  nothing  but  a  minute  amount 
of  the  vapor  of  mercury.  A  perfect  vacuum  would  be  a 
space  containing  nothing ;  but  such  a  condition  can  not  be 
reached.  All  that  we  can  arrive  at  is  a  space  containing 
only  a  very  minute  amount  of  gases  or  vapors. 

Uses  of  the  Barometer. — The  instruments  ordina- 
rily sold  as  mercurial  barometers  contain  a  tube  like  one  or 
the  other  of  those  shown  in  Fig.  106,  carefully  filled  with 
mercury,  all  air  being  removed.  A  scale  along  the  upper 
part  of  the  tube  marks  the  height  of  the  mercury.  This 
height  varies  from  time  to  time,  because  of  changes  in  the 
atmospheric  pressure  accompanying  changes  of  weather.  In 
general,  a  rapid  or  considerable  falling  of  the  mercury  ac- 
companies a  storm  and  a  rise  of  temperature ;  while  a  con- 
siderable rise  is  usually  accompanied  or  followed  by  fair  and 
cooler  weather.  The  weather  can  not,  however,  be  predicted 
closely  from  readings  of  the  barometer  alone.  Rapid  and 
extreme  changes  of  barometer  generally  indicate  and  accom- 
pany violent  winds.  The  barometer  is  also  used  to  measure 
the  heights  of  mountains,  as  explained  on  page  225. 

The  Aneroid  Barometer. — An  instrument  known  as 
the  Aneroid  (without  moisture)  Barometer  is  very  conven- 
ient for  many  purposes.  It  is  light,  compact,  and  easily 
carried,  and  thus  forms  a  desirable  substitute  for  the  mercu- 
rial barometer,  which  is  awkward  and  heavy,  although  more 
accurate. 


THE  ANEROID  BAROMETER. 


205 


A  flat,  thin-walled,  circular  metal  box  (two  to  five  inches  in  diam- 
eter), with  a  corrugated  surface,  is  hermetically  sealed,  after  the  air  has 
been  exhausted  from  within  it,  in  order  to  prevent  the  indications  from 
being  affected  by  the  varying  pressure  of  this  air  under  change  of 
temperature.  When  the  atmospheric  pressure  increases,  the  sides  of 
the  box  are  thereby  forced  farther  inward ;  and  when  this  pressure  is 
lessened,  they  spring  outward,  the  amount  of  motion  being  proportional 
to  the  change  of  pressure.  To  indicate  this  motion,  a  mechanical 
arrangement  of  levers,  etc.,  is  connected  with  the  box  in  such  a  way 
that  the  compression  and  expansion  move  a  pointer  playing  over  a 
graduated  dial.  From  this  dial  the  pressure  may  be  read  directly. 

To  understand  fully  the  principle  of  the  aneroid,  which  is  often 
carried  in  the  pocket  to  determine  heights  above  sea-level,  the  pupil 
must  examine  an  instrument  for  himself. 

QUESTIONS.— Prove  that  gases  have  weight.  Why  does  the  atmosphere  exert  a 
pressure  on  objects  within  it  ?  In  what  direction  is  the  atmospheric  pressure  ? 
What  is  illustrated  by  the  Magdeburg  hemispheres.  Describe  several  experi- 
ments illustrating  the  pressure  of  the  atmosphere.  Do  all  gases 
transmit  pressure  according  to  the  same  law  as  liquids  ?  Do  all 
fluids?  What  is  a  fluid? 

Describe  the  filling  and  inversion  of  the  tube  in  the  Torricellian 
experiment.  What  keeps  the  mercury  from  falling  inside  the  tube 
to  the  level  of  the  mercury  outside  ?  If  a  barometer-tube  were 
placed  under  the  receiver  of  an  air-pump  and  all  the  air  pumped 
out,  where  would  the  mercury  stand  in  the  tube  ?  Why  ?  How 
high,  on  the  average,  does  the  mercury  stand  in  a  baror.ieter- 
tube  ?  Why  does  it  vary  in  height  ?  What  is  meant  by  a  vacuum  ? 
Has  a  perfect  vacuum  ever  been  attained  ?  What  more  does  the 
ordinary  form  of  barometer  possess  than  the  single  tube  and 
cistern  represented  in  Fig.  106  ?  Enumerate  the  uses  of  the 
barometer.  Explain  the  principle  of  the  aneroid  barometer. 


COMPRESSIBILITY  AND  EXPANSION  OF 
GASES. 

Gases  are  compressible.  —  The  pneumatic 
syringe,  shown  in  Fig.  107,  is  a  glass  tube  in  which 
a  tight-fitting  piston  can  be  pushed  down.  Air  or 
other  gas  may  be  inclosed  between  the  piston  and 
lower  end  of  the  tube,  with  no  chance  for  escape. 
Push  down  the  piston,  the  air  is  reduced  in  volume  —  i.  e, 
is  compressed. 

Press  an  empty  tumbler,  mouth  downward,  into  water. 


FIG.  107. 


SYRINGE. 


206 


LIQUIDS  AND  GASES. 


Notice  that  the  water  rises  somewhat  in  the  tumbler,  com- 
pressing the  air.     Try  the  same  experiment  with  mercury. 

Law  of  Compressibility. — Fig.  108  shows  a  vertical 
glass  tube  bent  at  the  bottom,  open  at  the  end  B,  and  closed 
at  D.  The  tube  is  at  first  full  of  air  or  other  gas.  A  scale 
is  placed  along  each  branch.  A  little  mercury  is  then  poured 
in  at  B,  thus  separating  the  air  in  the  closed  branch,  D  C, 
from  the  outside  air,  so  that  no  air  can  enter  the 
closed  branch  or  escape  from  it  during  the  experi- 
ment. The  mercury  stands  at  nearly  the  same 
level  at  A  and  C,  and  therefore  does  not  exert 
any  pressure  on  the  inclosed  air. 

The  air  in  D  C  is  now  under  the  pressure  of  the  atmos- 
phere at  the  time,  for  the  atmosphere  is  pressing  down  on 
the  mercury  at  A,  and  the  pressure  is  transmitted  through 
the  mercury  to  the  gas  at  C.  This  pressure  may  be  as- 
sumed, for  our  experiment,  to  be  equal  to  that  of  about 
30  inches  of  mercury.  Read  now  the  heights  of  the  mer- 
cury at  A  and  C  on  the  scale  between  the  tubes.  They 
will  be  nearly  the  same.  Read  also  the  height  of  the  mer- 
cury at  C  on  the  scale  at  the  right  of  D  C.  This  scale  is 
numbered  from  the  top  D  downward,  and  measures  off 
the  volume  of  the  air  between  D  and  the  top  of  the  mer- 
cury. Suppose,  then,  that  A  and  C  read  2  on  the  middle 
scale,  and  C  reads  42  on  the  volume  scale.  Then  the  press- 
ure of  the  inclosed  air  is  30  inches  of  mercury,  and  the 
volume  is  42  units. 

Pour  in  more  mercury  until  the  mercury  in  the  open 
arm  stands  at  a  height  of  30  inches  above  that  in  the  closed 
arm — for  instance,  suppose  that  the  first  height  is  46  and 
the  second  16,  on  the  middle  scale,  and  that  the  reading 
in  the  closed  arm  is  21  on  the  volume  scale.     Then  the 
volume  has  been  reduced  to  21.    What  is  the  pressure? 
The  mercury  column  is  exerting  a  pressure  of  46  —  16  = 
30  inches,  by  its  own  weight.     In  addition  to  this,  it  is  transmitting 
the  atmospheric  pressure  of  30  inches.     Hence  the  pressure  on  the 
gas  at  the  level  of  the  mercury  in  the  closed  arm  is  30  +  30  =  60  inches. 
The  pressure,  then,  has  been  doubled,  and  the  volume  thereby  halved. 
Pour  in  more  mercury  until  A.  stands  60  inches  above  C,    Suppose 


Fio.  108. 


BOYLE'S  LAW.  207 

that  the  pressure  scale  then  reads  79*5  inches  and  19'5  inches,  and  that 
the  volume  scale  reads  14.  Then  the  mercury-pressure  is  79*5  —  19*5 
=  60  inches,  and  the  total  pressure  is  30  +  60  =  90  inches.  The  vol- 
ume is  14.  The  pressure  has  then  been  trebled,  and  the  volume  re- 
duced to  one  third. 

In  general,  it  will  be  found  that,  however  much  mercury 
is  poured  in,  the  volume  of  the  compressed  air  will  be  in- 
versely as  the  pressure  upon  it,  if  we  keep  the  air 
at  a  constant  temperature.  The  law  of  the  com- 
pressibility of  gases,  then,  is  as  follows : 

With  a  constant  mass  of  gas  at  a  constant  tem- 
perature, the  volume  is  inversely  as  the  pressure 
upon  it. 

This  law  is  very  nearly  true  for  all  gases,  but 
there  are  slight  variations  from  it.  It  is  called  the 
law  of  Boyle,  or  sometimes  the  law  of  Mariotte,  from 
the  names  of  its  discoverers. 

The  apparatus  of  Fig.  108  illustrates  the  law 
only  when  the  pressure  is  greater  than  that  of  the 
atmosphere.  Fig.  109  shows  an  apparatus  for  prov- 
ing the  same  law  for  smaller  pressures.  A  glass 
tube,  A  B,  closed  at  the  top,  is  filled  with  mercury, 
like  a  barometer-tube,  and  inverted  in  the  deep 
cistern  of  mercury,  E  F.  Then  a  little  air  is  al- 
lowed to  bubble  up  into  the  tube  through  the 
mercury,  collecting  above  it  as  shown  at  A  B. 

EXPERIMENT. — Push  the  tube  down  until  the  mercury 
within  it  stands  at  the  same  level  as  that  outside.    Then  the 
pressure  on  the  gas  is  equal  to  that  of  the  atmosphere,  or  30 
inches  of  mercury.     Measure  the  volume  of  the  air  by  read-     FlG  109 
ing  off  from  a  scale  beside  or  upon  the  tube  the  distance 
from  A  to  the  mercury  surface  in  the  tube.     If,  now,  the  tube  is 
lowered,  the  air  will  be  compressed.     If  it  is  raised,  the  air  will  ex- 
pand.    Raise  the  tube  somewhat.     Measure  the  volume  A  B  from  A 
to  the  top  of  the  mercury  column  (left-hand  position  in  the  figure) ; 
also  the  distance  from  B  to  E,  the  mercury  surface  in  the  cistern. 
The  pressure  of  the  air  is  now  less  than  that  of  the  atmosphere  by 


208  LIQUIDS  AND  GASES. 

the  pressure  of  the  mercury  column  whose  height  is  BE;  for  the 
atmospheric  pressure  transmitted  from  the  outside  surface  of  the  liquid 
in  E  through  the  mass  of  liquid  and  into  the  tube  is  balanced  in  part 
by  the  pressure  due  to  the  weight  of  the  column  B  E.  The  pressure 
is,  then,  30  inches  minus  B  E  (expressed  in  inches). 

For  example,  if  B  E  =  5  inches,  the  pressure  is  now  30  —  5  =  25 
inches.  Suppose  the  first  volume  was  42,  then  the  present  volume  will 
be  found  to  be  50-4.  Now,  50'4  :  42  =  6  :  5,  and  25  :  30  =  5  :  6.  That 
is,  the  volume  is  inversely  as  the  pressure.  If  the  tube  be  raised  still 
higher,  as  shown  in  the  second  position  in  Fig.  109,  the  air  will  expand 
further,  and  the  mercury  stand  at  a  still  higher  point,  D.  Suppose 
that  D  E  =  15  inches.  Then  the  pressure  will  be  30  —  15  =  15  inches, 
or  one  half  the  original.  The  volume  will  be  found  to  be  84  —  that  is, 
double  the  original.  Thus  the  same  law  holds  ;  for  the  atmospheric 
pressure,  under  which  we  start  to  go  either  one  way  or  the  other,  is  no 
natural  starting-point,  but  merely  a  pressure  which  happens  to  exist 
at  the  earth's  surface. 

In  all  these  cases,  the  pressure  exerted  by  the  gasjs  of 
course  exactly  equal  and  opposite  to  the  pressure  upon  the 
gas.  Otherwise,  there  would  not  be  equilibrium. 

Gases  expand.  —  We  have  seen  how,  by  increasing  the 
pressure  upon  them,  we  can  compress  gases.  Let  us  study 
the  effect  of  removing  the  pressure. 

EXPERIMENT.  —  Close  the  opening  of  a  rubber  toy  balloon,  after 

allowing  most  of  the  gas  to  escape  ;  or  tie  up  the  end  of  one  of  the 

small  rubber  bags  used  on  children's  toy 

3gi_  whistles,  or  the  end  of  a  moistened  bladder, 

leaving  a  little  air  inclosed.    Put  this  under 

I  in  the  receiver  of  an  air-pump.     The  balloon 

is  loose  and  lies  in  folds,  as  in  Fig.  110  ; 
the  air  inside  and  outside  of  it  is  at  the 
same  pressure,  that  of  the  atmosphere  at 
the  time.  Now  work  the  pump.  Notice 
how  the  balloon  swells  out  more  and  more 
as  you  proceed.  What  is  taking  place? 

°f  the  a 


FIG.  HO.-EXPANSIONOF  AIR. 

the  receiver,  thus  reducing  the  pressure. 

The  air  pressure  within  the  balloon  is  no  longer  balanced  by  that  out- 
side, and  motion  ensues.  The  air-molecules  within  the  balloon  force 
one  another  farther  and  farther  apart  —  that  is,  the  gas  expands. 


EXPANSION  OF  GASES. 


209 


FIG.  111. 


FIG.  112. 


How  much  does  it  expand  I  Stop  pumping,  so  that  the  pressure 
on  the  balloon  may  be  constant.  The  air  in  it  expands  until  its  press- 
ure inside  the  balloon  is  just  equal  to  that  outside,  allowing  of  course 
for  any  elastic  force  produced  by  the  rubber  if  it  is  stretched.  The 
more  you  pump,  the  less  the  outside  pressure,  and  the  more  the  air  in- 
side must  expand  to  reduce 
its  pressure  to  equal  that  out- 
side. This  would  continue 
indefinitely,  either  until  the 
balloon  was  expanded  suffi- 
ciently to  fill  the  whole  re- 
ceiver, or  until  it  burst. 

Fig.  Ill  suggests  a  sim- 
pler way  of  performing  this 
experiment — suck  the  air  out 
of  the  bottle  through  the  tube 
E.  Fig.  112  illustrates  the 
principle  in  another  way. 
The  glass  bulb  F  full  of  air 
(an  inverted  test-tube  will  answer)  is  placed  inside  the  bottle,  with  its 
open  end  down,  and  immersed  in  a  shallow  layer  of  water  at  B.  C  is 
a  plug  closing  the  second  opening  in  the  stopper.  On  sucking  the  air 
out  of  the  bottle  by  the  mouth  at  the  tube  E,  the  air  in  the  bulb  will 
expand,  as  shown  by  its  bubbling  through  the  water. 

The  apparatus  of  Fig.  109  also  illustrates  the  expansion 
of  gases. 

Expansion  will  continue  indefinitely — that  is,  a  gas 
will  continue  to  expand  as  long  as  we  go  on  diminishing  the 
pressure.  Suppose  we  had  a  large  air-tight  box  and  ex- 
hausted all  the  air  from  it,  so  that  it  was  really  empty — i.  e., 
was  a  vacuum.  Then  suppose  we  admitted  a  small  bubble 
of  any  gas.  Even  so  minute  a  portion  would  rapidly  expand 
to  occupy  the  whole  box ;  and  this  would  be  true,  however 
small  the  amount  of  gas  and  however  immense  the  box,  pro- 
vided there  were  no  disturbing  forces  like  gravity.  This  fact 
about  gases  is  sometimes  expressed  by  saying  that  gases  tend 
to  expand  indefinitely  ;  by  which  is  meant  that  they  will  so 
expand  unless  prevented  by  some  external  force. 

Why  do  gases  thus  expand  if  left  to  themselves  ?    This 


210  LIQUIDS  AND  GASES. 

has  already  been  illustrated  at  page  72.  By  carefully  re- 
viewing the  statement  there  made,  you  will  see  that  it  is 
a  necessary  consequence  of  the  supposed  continual  heat 
vibration  of  the  molecules  of  the  gases. 

As  all  gases  with  which  we  deal  are  under  some  compressive  force 
greater  or  less  than  that  of  the  atmosphere,  they  must  all  be  constantly 
exerting  an  expansive  or  outward  force  or  pressure.  Of  this  we  have 
familiar  evidence  in  the  explosive  force  of  air  or  steam  under  great 
compression  in  air-guns  and  steam-boilers,  as  well  as  in  the  gases  gen- 
erated behind  a  cannon-ball  by  the  burning  powder,  etc. 

Absorption  of  Gases. — The  reduction  of  the  volume 
of  gases  may  also  be  shown  in  an  interesting  way  by  the  fol- 
lowing experiment : 

EXPERIMENT. — Fill  with  mercury  a  glass  tube  an  inch  in  diameter 
and  four  or  more  inches  long.  Invert  it  in  a  vessel  of  mercury.  In- 
troduce into  the  tube  over  the  mercury  enough  ammonia  or  carbonic 
acid  gas  to  displace  nearly  all  the  mercury.  Heat  thoroughly  a  small 
piece  of  wood  charcoal  in  the  flame  of  a  Bunsen  or  alcohol  lamp  (see 
page  230).  Cool  it  by  plunging  it  into  the  mercury,  and  then  let  it  float 
up  into  the  tube.  The  charcoal  will  soon  absorb  a  large  portion  of  the 
gas,  and  the  mercury  will  rise  in  the  tube.  The  gas  appears  in  this 
case  to  be  simply  reduced  in  volume  by  a  peculiar  condensing  action 
of  the  charcoal,  and  not  to  be  chemically  acted  upon.  It  will  be  given 
off  again  by  the  charcoal  upon  heating.  The  preliminary  heating  was 
to  expel  gases  already  condensed  within  the  charcoal. 

Gases  are  also  reduced  in  volume  by  solution  in  liquids. 
If  water  that  has  been  standing  in  the  air  for  a  while  be 
boiled,  it  may  be  found,  with  suitable  apparatus,  that  a  con- 
siderable volume  of  air  which  was  held  in  solution  is  given 
off.  If  a  tumblerful  of  cool  water  be  drawn  from  the  well 
or  pipes  and  allowed  to  stand  in  a  warm  room  for  some 
time,  bubbles  of  air  will  be  found  upon  the  inner  surface  of 
the  glass.  This  is  air  held  in  solution  by  the  cool  water  and 
given  out  by  it  as  it  becomes  warmer.  Fish  breathe  such  air 
mechanically  entangled  in  water.  How  ?  The  foam  and 
bubbling  of  soda  and  other  mineral  water  is  due  to  the  giv- 


THE  AIR-PUMP.  211 

ing  off  of  carbon-dioxide  (carbonic  acid  gas)  held  in  solu- 
tion under  pressure. 

QUESTIONS.— Describe  the  experiments  showing  the  compressibility  of  gases. 
State  the  law  of  compressibility.  Describe  an  experiment  proving  this  law  for 
pressures  below  one  atmosphere  ;  for  pressures  above  one  atmosphere.  Why 
do  we  find  it  convenient  to  start  with  the  atmospheric  pressure  rather  than 
some  other  ?  Why  is  it  necessary  to  confine  gases  on  all  sides  in  order  to  re- 
tain them  ?  What  would  an  unconfined  gas  not  affected  by  gravitation  do  ? 
What  is  meant  by  the  statement  that  gases  tend  to  expand  indefinitely  ? 

Are  all  gases  with  which  we  have  to  deal  exerting  an  outward  elastic  pressure  ? 
How  is  this  pressure  explained  on  the  molecular  theory  ?  Suppose  a  barometer- 
tube,  with  the  mercury  standing  at  30  inches,  be  sealed  up  in  a  glass  case  full 
of  air  into  and  out  of  which  no  air  can  go.  At  what  height  will  the  mercury 
stand  ?  The  outside  atmospheric  pressure  can  not  get  at  the  cistern  when  thus 
sealed.  Why,  then,  does  not  the  mercury  fall  ?  What  does  this  illustrate  ? 

Describe  experiments  illustrating  tne  expansive  pressure  of  gases  ;  an  experiment 
showing  the  absorption  of  gases  by  solids.  Are  gases  absorbed  by  liquids  ?  How 
does  absorption  illustrate  the  compressibility  of  gases  ?  Why  is  a  boiler  full  of 
steam  at  100  pounds  pressure  more  dangerous — i.  e.,  why  does  it  possess  more 
energy— than  if  filled  with  cold  water  under  the  same  atmospheric  pressure  ? 


PUMPS  AND  SIPHONS. 

The  Air-Pump. — Fig.  11,  on  page  173,  illustrates  a 
simple  form  of  air-pump.  The  use  of  this  particular  form 
is  to  remove  air  from  apparatus  for  such  experiments  as 
many  already  described.  The  air-pump  has,  however,  very 
important  applications  in  commercial  work,  for  removing 
air  or  other  gases  from  apparatus  of  various  kinds,  such  as 
the  evaporating  tanks  in  sugar-refining,  the  condensers  of 
steam-engines,  the  globes  of  incandescent  electric  lamps, 
parts  of  ice-making  machinery,  etc.  Air-pumps  are  of  two 
classes — those  whose  parts  are  all  solid,  and  those  whose 
action  depends  on  the  use  of  mercury.  The  first  kind  only 
will  be  described  here,  and  the  common  school  air-pump 
will  be  selected  as  a  type.  Pumps  of  larger  size,  which  are 
usually  run  by  steam-power,  are  similar  in  principle. 

Fig.  113  shows  a  vertical  section  of  the  pump  illustrated  on  page 
173.  R  is  the  receiver,  N  M  the  plate  on  which  R  stands,  O  the  cen- 
tral tube  passing  through  the  plate  and  base  to  the  pump  proper,  P'. 
S  is  a  screw  stop-cock,  When  turned  forward,  it  closes  the  tube  at  its 


212 


LIQUIDS  AND  GASES. 


point,  so  that  no  air  can  pass  up  into  the  receiver  from  the  pump  or 
outside.  H  is  the  handle  of  the  pump,  and  moves  the  piston  P'  in 
and  out  of  the  cylinder. 

Start  with  S  open  and  the  piston  down  in  the  cylinder,  as  shown 
in  the  upper  figure  at  P',  all  being  at  rest.  Then  the  valve  at  V  is 

closed,  and  also  the  one  at  a'  in 

v^  the  piston,  their  weight  keeping 

'  * D  them  down.     The  receiver,  pipe, 

and  pump,  are  fall  of  air  at  the 
atmospheric  pressure.  Let  H  be 
pulled  backward,  moving  in  the 
direction  of  the  arrow  in  the 
second  figure.  The  space  be- 
tween the  lower  valve  b  and  the 
piston  P  will  thus  be  increased. 
The  air  will  expand  to  fill  this 
space,  and  will  be  thereby  re- 
duced in  pressure.  It  will  there- 
fore press  upon  the  front  side 
of  b  less  than  the  air  in  the  re- 
ceiver presses  upon  the  rear  side. 
Hence  b  will  be  pushed  open 
into  the  position  b",  and  will  be  held  open  as  long  as  H  is  moving 
outward.  Thus  all  the  air  in  the  receiver,  pipes,  and  pump  below  the 
piston,  continues  to  expand  as  long  as  the  piston  moves.  The  valve  a 
will  be  kept  closed  throughout  by  its  weight  and  the  atmospheric 
pressure  outside. 

When  P  stops  at  the  end  of  the  stroke,  b"  will  fall  into  the  closed 
position  b'  or  b'"  by  its  weight.  The  return  stroke  is  made  by  pushing 
H  inward  as  shown  by  the  arrow  in  the  lower  figure.  Valve  b  remains 
closed.  Valve  a  remains  closed  also  at  first,  until  the  air  between  V" 
and  the  piston  P'"  is  reduced  to  such  a  volume  that  its  pressure  is 
again  equal  to  that  of  the  atmosphere  and  just  enough  more  to  lift  the 
weight  of  the  valve  a.  Then,  as  the  piston  goes  down  farther,  this  air 
opens  a  into  the  position  a'",  and  continues  to  escape  through  it  until 
the  piston  stops  at  the  bottom  of  the  cylinder,  when,  of  course,  a  closes 
into  its  first  position  by  its  weight. 

The  operation  is  then  repeated.  As  H  is  drawn  out  again,  the  air 
in  the  receiver  opens  b  when  the  pressure  of  the  air  below  P  is  reduced 
by  its  expansion  to  a  little  less  than  that  in  0,  so  that  the  weight  of  the 
valve  can  be  lifted.  The  receiver  air  then  holds  b  open  and  expands 
into  the  pump  until  the  out-stroke  is  completed.  Then  b  closes,  the 


FIG.  113. — PRINCIPLE  OP  AIR-PUMP. 


THE  LIFTING-PUMP. 


213 


in-stroke  begins,  a  presently  opens,  more  air  passes  out  by  the  moving 
piston  until  the  in-stroke  is  completed,  and  the  operation  begins  anew. 

Thus  at  each  stroke  a  certain  fraction  of  the  air  is  removed.  Sup- 
pose this  fraction  to  be  -fa.  Then  the  first  stroke  removes  fa  of  the 
air  and  1%  remain.  The  second  stroke  removes  -fa  of  the  remainder — 
i.  e.,  fa  x  1%  =  Ttju  °f  the  whole.  There  therefore  remains  -fa  —  Tthr  or 
^/o  after  the  second  stroke ;  -i70^r,  or  say  -j2^,  after  the  third,  and  so 
on.  You  will  thus  see  that  a  smaller  fraction  of  the  original  air  is 
removed  each  time,  and  that  we  can  never  remove  it  all. 

To  obviate  the  difficulty  of  lifting  the  weight  of  the  valves  which 
interferes  with  very  thorough  exhaustion,  automatic  arrangements  of 
various  kinds  are  used  in  specially  fine  pumps. 

The  Lifting-Pump. — Perhaps  the  most  familiar  of  the 
many  forms  of  pumps  is  that  used  for  raising  water  from 
wells,  known  as  the  lifting-pump.  The  glass  model  shown 
in  the  left-hand  figure  of  apparatus  numbered  12  (page  173), 
illustrates  clearly  its  operation. 
The  action  of  the  pump  will  be 
described,  however,  with  refer- 
ence  to  Fig.  114,  which  shows 
an  actual  form  of  lifting-pump 
for  water. 

The  valves  of  the  lifting-pump 
work  in  precisely  the  same  way  as 
those  described  for  the  air-pump.  Let 
us  suppose  the  pump  full  of  water  and 
the  handle  A  stationary.  Then  the 
upper  valve  a  in  the  piston,  and  the 
lower  valve  b  (fixed  in  position  in  the 
bottom  of  the  pump),  close  of  their 
own  weight.  The  water  can  not  then 
escape  downward  through  them,  as 
they  and  the  piston  are  made  water- 
tight. But  why  does  the  water  stand 
up  to  b  in  the  pipe  above  the  surface 
of  the  supply  W?  Why  does  it  not 

run  down  and  leave  the  pipe  empty — i.  e.,  a  vacuum  f  "Why  does  the 
mercury  stand  at  a  height  of  30  inches  in  the  barometer-tube  (Fig. 
106)?  Why  does  the  water  fill  the  inverted  tube  Fig.  105  and  the 


FIG.  114.— SECTION  OP  LIFTING- 
PUMP. 


214  LIQUIDS  AND  GASES. 

tumbler  of  the  experiment  on  page  202  ?  The  water  is  kept  up  in  the 
pipe  by  the  atmospheric  pressure  when  the  pipe  has  once  been  filled, 
provided  there  is  no  leak.  The  atmosphere  presses  down  on  the  water 
surface  at  W,  and  this  pressure  is  transmitted  through  the  water  to 
the  bottom  of  the  pipe  and  up  through  the  water  in  the  pipe  to  the 
bottom  of  the  valve.  The  valve  a  is  then  pressed  upward  on  its  under 
side  by  the  atmospheric  pressure  less  that  due  to  the  column  of  water 
whose  vertical  height  is  from  b  to  the  surface  of  W.  It  is  pressed 
downward  by  the  atmosphere  plus  the  column  above  b. 

Now,  push  down  the  handle  A  so  as  to  cause  C  to  rise,  thereby 
raising  P.  Call  this  a  forward  stroke.  As  P  rises,  the  water  forced 
up  by  the  atmosphere  follows  it,  pressing  open  &,  which  is  hinged  at 
one  side,  and  thus  keeps  the  pump  full  up  to  the  piston.  The  valve  a 
is  kept  closed  by  its  own  weight  and  part  of  the  atmospheric  pressure. 
At  the  end  of  the  forward  stroke,  P  stops  and  b  closes  by  its  weight. 

Then  the  return-stroke  begins.  As  b  is  closed  and  kept  so  by  its 
weight  and  by  atmospheric  pressure,  the  water  above  it  can  not  escape. 
As  P  descends,  therefore,  the  water  beneath  forces  a  open  and  escapes 
through  it  to  the  upper  side  of  P.  When  the  return-stroke  is  com- 
pleted, P  stops  and  a  closes  by  its  weight.  A  forward  stroke  is  then 
begun  and  goes  on  as  before,  the  water  above  P  overflowing  at  S. 

The  amount  of  work  done  at  each  stroke  in  steady 
pumping  is  equal  to  the  work  required  to  lift  vertically 
from  W  to  S,  against  its  weight,  the  mass  of  water  which 
overflows ;  and  in  addition  to  do  all  the  work  of  friction  and 
acceleration.  The  actual  mass  of  water  overflowing  is,  of 
course,  not  lifted  from  W  at  that  particular  stroke ;  but  the 
work  done  in  lifting  all  the  water  in  the  pump  the  short 
distance  through  which  it  rises  is  equal  to  that  which  would 
be  done  in  lifting  the  overflowing  mass  from  W  to  S. 

What  is  the  source  of  energy  which  does  this  work  ?  It 
is  the  source  which  acts  on  the  handle  A,  whatever  that 
source  may  be — e.  g.,  a  man  or  an  engine.  It  is  not  the  at- 
mosphere or  gravity.  Without  the  atmosphere,  the  lifting- 
pump  would  not  work,  for  the  water  would  not  stay  up 
nnder  the  valve ;  but  the  atmosphere  is  not  the  source  of 
the  energy  which  does  the  work.  The  pump  does  just  as 
much  work  against  the  atmosphere  as  the  atmosphere  does 


PRINCIPLE  OF  THE  LIFTING-PUMP.  215 

upon  the  water  in  the  pump — i.  e.,  at  each  stroke,  as  much 
energy  is  restored  to  the  atmosphere  as  is  taken  from  it. 

All  the  work  (except  a  little  friction)  is  done  on  the  for- 
ward stroke.  As  this  stroke  is  progressing,  the  upward 
pressure  on  the  bottom  of  the  piston  is  equal  to  the  atmos- 
pheric pressure  minus  the  pressure  due  to  the  column  of 
water  from  P  to  W.  The  downward  pressure  on  the  top  of 
the  piston  is  that  of  the  atmosphere  plus  that  due  to  the 
column  of  water  above  P.  The  piston  is  therefore  pressed 
downward  on  the  whole  by  a  pressure  due  to  the  column  of 
water  lifted.  The  force  by  which  P  must  be  pulled  up  is 
then  equal  to  its  area  multiplied  by  the  intensity  of  the 
pressure  due  to  a  water  column  of  the  height  P  W.  The 
work  done  at  each  stroke  is  equal  to  this  force  multiplied  by 
the  distance  through  which  P  moves. 

The  action  of  the  atmosphere  may  be  regarded  as  simply 
holding  the  water  up  in  the  pump  and  pipe.  Cohesion 
would  do  equally  well  if  the  water  cohered,  and  also  adhered 
to  the  piston  with  such  force  that  its  own  weight  would  not 
pull  it  away. 

How  is  the  pump  filled  in  the  first  place  ?  If  the  piston  and  valves 
work  air-tight,  we  may  start  with  the  pump  empty — i.  e.,  containing 
nothing  but  air  down  to  the  level  of  W.  Then,  on  raising  and  lower- 
ing the  piston,  this  air  will  be  pumped  out  and  the  water  will  follow  it 
up  into  the  pump — that  is,  the  pump  will  act  as  an  air-pump  until  all 
the  air  is  removed,  and  then  it  will  be  full  of  water  and  act  as  a 
water-pump.  If  the  piston  and  valve  do  not  work  air-tight,  some 
water  is  poured  into  the  top  of  the  pump.  This  serves  temporarily  to 
seal  up  the  valves  and  piston  so  that  they  will  not  leak  air,  as  water 
leaks  through  small  crevices  more  slowly  than  air.  The  pump  then 
works  as  an  air-pump  until  the  water  fills  it.  If  the  pump  leaks 
through  the  lower  valve  or  at  any  point  of  the  pipe  below  it,  air  will  be 
drawn  in  and  the  water  will  run  out  when  the  pump  is  not  in  use.  The 
pump  is  then  said  to  be  "  run  down."  To  prevent  freezing,  the  water  is 
often  let  out  purposely  by  opening  both  valves  or  otherwise  admitting 
air.  The  lower  valve  is  usually  provided  with  a  point  projecting  upward 
and  backward,  so  that  when  the  piston  is  forced  as  far  down  as  possible 
it  presses  upon  this  point  in  such  a  way  as  to  hold  both  valves  open. 


216 


LIQUIDS  AND  GASES. 


The  Limit  of  Height  P  W  at  which  the  pump  can  be 
placed  above  the  level  of  the  supply  is  about  34  feet,  for  the 
pump  will  not  work  above  the  height  at  which  the  water 
can  be  sustained  by  the  atmospheric  pressure.  We  have 
seen,  on  page  203,  that  this  is  34  feet.  In  practice,  however, 
the  lifting-pump  will  often  cease  to  work  at  a  less  height 
than  this,  as  the  atmospheric  pressure  will  sometimes  bal- 
ance only  about  30  feet  of  water.  Of  course,  the  greater 
the  height  P  W,  the  larger  the  piston,  and  the  smaller  the 
pipe,  the  harder  the  pump  works. 

The  pump-handle,  as  shown  in  Fig.  114,  is  a  lever,  and 
thus  affords  the  mechanical  advantage  of  using  a  small 

force  through  a  long  dis- 
tance to  do  the  work  of 
lifting  the  piston  through 
a  short  distance  against  a 
large  force. 

The    Force-Pump. — 

The  glass  apparatus  illus- 
trated in  the  left-hand 
figure  of  No.  12,  page  173, 
clearly  shows  the  action  of 
the  force-pump.  Fig.  115 
is  a  sketch  of  an  actual 
pump.  This  kind  of  pump 
is  used  for  forcing  water 
upward,  when  it  is  desired 
to  deliver  the  water  at  a 
point  at  which  it  is  not 
convenient  to  locate  the 
pump,  when  the  water  is  to 
be  raised  above  the  limiting 

height  of  the  lifting-pump,  or  when  water  is  to  be  delivered 
under  great  pressure,  as  in  fire-engines  and  other  forms  of 
pumping-engines. 


FIG.  115. — SECTION  OP  FORCE-PUMP. 


THE  FORCE-PUMP.  217 

The  piston  P  is  solid  and  is  raised  and  lowered  by  the  lever  A  C  B 
through  the  connecting  rod  C  D.  Valves  opening  upward  (usually 
hinged  at  one  side)  are  placed  at  a  and  b.  Assume  the  pump  to  be 
full  of  water  in  all  the  shaded  parts.  No  water  is  supposed  to  go 
above  the  piston.  Let  an  up  stroke  of  the  piston  be  started.  The 
valve  a  will  close  by  its  weight  and  that  of  the  water  above  it,  and  the 
water  from  the  supply  W  will  be  forced  up  by  the  atmosphere  through 
b,  which  will  thus  be  held  open.  At  the  end  of  the  up  stroke,  the 
valve  b  will  close  by  its  weight.  At  the  beginning  of  the  down  stroke, 
the  piston  will  force  the  water  out  ahead  of  it,  and,  as  b  is  closed  the 
tighter  by  this  pressure,  the  water  can  escape  only  by  opening  a  and 
passing  through  it  into  the  delivery-pipe  H  S.  This  pipe  leads  off  to 
the  point  at  which  it  is  desired  that  the  water  shall  be  delivered.  It 
may  be  as  high  or  as  long  as  desired,  the  only  effect  of  increased  length 
and  height  being  to  require  the  application  of  more  energy  at  A  and 
greater  strength  of  pump  and  pipes. 

The  Air-Dome,  shown  in  Fig.  116,  is  usually  connected 
with  powerful  force-pumps.  Its  object  is  to  steady  the 
pressure  at  which  the  water  goes  through  the  delivery-pipe. 

Let  A  B  be  a  section  of  some  horizontal  portion  of  the  delivery- 
pipe  H  S  near  the  pump.     A  branch  pipe  turns  upward  from  A  B,  and 
upon  this  is  placed  the  air-tight  hollow  dome  of  metal  C  D  E.     This 
dome  is  full  of  air.     When  the  pump  makes  a  down 
stroke,  it  forces  water  violently  into  the  delivery- 
pipe,  and  would  thus  greatly  increase  the  pressure 
and  give  a  violent  strain   to  all  the  piping.     The 
dome  reduces  this  shock,  for,  as  the  water  is  forced 
violently  in  at  A,  it  finds  the  escape  into  the  dome 
by  compressing  the  air  there  easier  than  the  violent 
passage  out  through  B.     The  sudden  rush  of  water 
passes  partly  into  the  dome,   rising  there  from  a      FIG  116— AIR- 
level  C  to  a  higher  one  D  and  compressing  the  air.  DOME. 

As  soon  as  the  down  stroke  ceases,  the  valve  a  closes 
and  the  compressed  air  in  the  dome  forces  the  water  out  through 
B,  lowering  it  to  its  former  level  at  C. 

This  operation  goes  on  at  each  double  stroke.  Thus  the  air-dome 
relieves  the  violence  of  the  shock  in  the  pipes  beyond  it,  and  to  some 
extent  also  in  the  pump  and  the  connecting  pipes.  It  also  makes  the 
rate  of  delivery  more  uniform,  as  owing  to  its  action  there  will  be  water 
flowing  through  B  during  the  up  stroke  when  there  would  be  none 
15 


218  LIQUIDS  AND  GASES. 

without  it.  This  dome  may  be  seen  on  steam  fire-engines,  and  on  al- 
most all  "  power  pumps  " — i.  e.,  pumps  run  by  steam-power. 

The  Siphon. — Bend  a  glass  tube,  one  or  two  feet  long 
and  a  quarter  of  an  inch  in  diameter,  as  shown  at  A  B  C, 
Fig.  117.  Leaving  it  full  of  air,  dip  one  end  into  a  ves- 
sel of  water  D  and  let  the  other  hang  out  into  the  air  or 
dip  into  another  dish  of  water  at  E.  No  action  will  take 
place.  Now  take  the  tube  out  and  fill  it  with  water.  Close 
each  end  with  a  finger  and  dip  one  into  D,  the  other  into 
E.  Water  will  flow  through  the  tube,  from  the  vessel  D  in 
which  the  water  surface  is  at  the  higher  level,  into  E,  in 
which  it  is  at  the  lower  level. 

Make  the  level  of  the  surfaces  in  D  and  E  the  same. 
The  flow  will  cease.  Leave  the  end  C  free  in  air.  The 

water  will  flow  freely  out  of  it, 
gradually  emptying  D.  Pull  the 
tube  up  until  A  is  out  of  water, 
or  let  the  action  go  on  until  the 
water  is  drawn  down  to  A.  Air 
will  enter,  filling  the  tube,  and 
the  action  will  cease.  Any  tube 
acting  in  this  way  is  called  a 
Siphon.  A  glass  tube  has  been 

FIG.  1 17.— SIPHONING.  r       . 

used  in  the  experiment  merely 

because  it  enables  the  operation  to  be  more  clearly  seen.  A 
tube  of  rubber  or  metal,  or  any  other  material,  will  give  the 
same  results. 

Why  does  the  water  flow  ?  In  the  first  place,  suppose  the  level  of 
the  water  in  D  and  E  to  be  the  same,  and  hence  no  flow  to  be  taking 
place.  The  water  still  fills  both  sides  of  the  tube  up  to  B.  It  is  re- 
tained there  by  the  atmospheric  pressure  on  D  and  E,  and  the  tube 
will  thus  be  kept  full  when  once  filled,  however  long  either  arm,  with- 
in the  limit  of  34  feet.  Next  suppose  one  surface,  E,  to  be  lower  than 
the  other,  D.  Then  at  the  top  section  B,  the  pull  on  the  water  toward 
E  is  that  due  to  the  column  of  water  whose  height  is  the  vertical  dis- 
tance from  B  to  E,  while  the  pull  toward  D  is  that  due  to  the  differ- 


THE  SIPHON. 


219 


ence  of  level  B  D.  There  is,  therefore,  a  resultant  pull  toward  the 
lower  level  of  an  amount  proportional  to  the  difference  of  these  two 
heights,  which  is  F  E,  the  difference  of  level  of  the  two  surfaces.  The 
water  will  therefore  flow  from  D  to  E  as  fast  as  this  force  can  draw  it 
against  the  resistance  due  to  friction  in  the  pipe,  etc. 

The  siphon  requires  the  atmospheric  pressure  merely  to  keep  the 
water  together  in  the  tube.  If  the  water  had  cohesion  enough  to  hold 
itself  together,  the  siphon  would  work  without  the  atmosphere.  In 
fact,  a  short  siphon  will  work  under  the  receiver  of  an  air-pump. 

The  Source  of  Energy  that  works  the  Siphon  is 

gravity,  the  force  being  the  weight  of  the  liquid.  The  mov- 
ing liquid  acquires  no  energy  from  the  atmosphere.  As  the 
working  force  is  proportional  to  the  difference  of  level  of 
the  surfaces  of  the  supplying  and  the  receiving  liquid,  it  is 
evident  that  the  greater  this  difference  of  level  the  faster 
the  siphon  will  work,  other  things  being  equal.  The  larger 
the  tube,  the  less  the  friction  and  the  faster  the  flow ;  but 
if  the  tube  be  very  large  and  the  flow  slow,  air  may  bubble 
up  into  the  siphon  and  stop  its  action. 

The  siphon  is  of  service  in  causing  a  flow  of  liquid  from  one  place 
to  another  when  a  pump  is  not  available;  in  emptying  a  vessel  in 
which  it  is  desired  not 
to  bore  a  hole  at  the 
bottom;  in  transferring 
acids  which  it  is  incon- 
venient or  dangerous  to 
handle,  etc.  The  form 
of  tube  used  may  be  any- 
thing that  is  convenient 
for  the  purpose  at  hand ; 
the  difference  of  level  is 

the  thing  essential  to  its  FIG.  IIS.-SECTION  OP  NATURAL  SIPHON. 

working. 

Crevices  in  rocks  sometimes  act  as  siphons  and  drain  underground 
cavities,  giving  rise  to  intermittent  springs.  In  the  section  shown  in 
Fig.  118,  the  water  derived  from  surface  drainage  will  rise  to  the 
level  B  L  in  the  reservoir  before  the  crevice  begins  to  discharge  it 
at  A.  Why  f  The  crevice  will  continue  to  drain  the  cavity  until  the 
level  is  reduced  to  A  L,  when  the  flow  ceases.  Why  1 


220  LIQUIDS  AND  GASES. 

QUESTIONS.— Describe  the  action  of  the  Air-Pump.  Would  the  air-pump  work  if 
gases  were  not  self -expansible  ?  Can  all  the  air  be  removed  from  a  vessel  by  a 
perfect  air-pump  ?  Why  ?  Describe  the  construction  of  the  Lifting-pump,  its 
mode  and  principle  of  action.  Would  the  pump  work  if  the  atmospheric  press- 
ure were  removed  ?  What  part  does  the  pressure  play  ?  Where  does  the  en- 
ergy come  from  which  lifts  the  water  ?  How  much  energy  must  be  supplied  at 
each  stroke  ?  Would  you  think  it  correct  to  say  that  in  raising  the  piston  of 
the  pump  the  atmospheric  pressure  was  partly  or  wholly  removed  by  that 
means  from  the  top  of  the  water  column  and  the  atmosphere  thus  permitted  to 
force  up  the  water  beneath  the  piston  ?  If  so,  show  that  the  work  done  upon 
the  atmosphere  in  that  operation  is  equal  to  that  done  by  it.  If  we  had  a 
liquid  endowed  with  strong  cohesion  and  adhesion,  could  it  be  pumped  in  vac- 
uo  ?  May  we  then  say  that  the  atmospheric  pressure  supplies  the  place  of  co- 
hesion in  the  action  of  the  pump  ?  What  is  the  average  highest  limit  at  which 
a  lifting-pump  can  be  worked  above  the  supply  ? 

Describe  the  form  and  action  of  the  Force-Pump.  Show  how  it  is  only  a  slight 
modification  of  the  lifting-pump.  Take  the  case  of  a  well  in  which  the  water 
stands  50  feet  below  the  surface,  and  suggest  some  way  of  pumping  the  water 
out.  Describe  the  action  of  the  Air-Dome. 

What  is  a  Siphon  ?  Describe  its  action.  Will  it  work  in  vacua  f  To  what  extent ': 
Why  does  it  depend  upon  the  atmosphere  ?  What  is  the  source  of  energy 
which  transfers  the  water  ?  The  water  at  the  lower  level  has  less  potential  en- 
ergy than  at  the  higher,  and  after  it  has  become  still  it  has  no  energy  of  on- 
ward motion  ;  what,  then,  has  become  of  the  energy  expended  upon  it  in  the 
siphon  ?  Would  the  water  be  warmer  after  passing  through  the  siphon  ? 
Should  you  expect  to  detect  the  difference  with  the  sense  of  touch  ?  Why  ? 
Some  miners  desire  to  empty  a  large  wooden  water-tank,  but  do  not  wish  to 
bore  a  hole  in  it,  and  have  no  pump  ;  they  are  at  a  loss  to  know  how  to  proceed. 
What  method  can  you  suggest  ?  Explain  intermittent  springs.  Ascertain  what 
the  Tantalus  Cup  is,  and  explain  its  action. 


DIFFUSION  OF  GASES. 

Diffusion  through  a  Porous  Partition. — In  Fig. 
119,  B  represents  a  porous  earthenware  jar,  such  as  is  used 
in  some  electric  batteries.  It  is  inverted,  and  its  open  end 
is  plugged  with  a  rubber  or  cork  stopper,  through  which 
passes  a  glass  tube,  C,  opening  into  the  jar  and  dipping  into 
a  colored  liquid  in  D.  A  large  glass  jar  or  wide-mouthed 
bottle,  A,  can  be  held  inverted,  as  shown,  over  B.  Let  A 
be  removed  and  held  over  a  hydrogen  generator  or  jet  of  il- 
luminating gas.  The  hydrogen  will  rise  and  fill  A.  Then 
let  A  be  carefully  pushed  down  over  B,  as  in  the  figure. 
Bubbles  of  gas  will  at  once  begin  to  come  up  through  the 
liquid  in  D,  showing  that  the  amount  and  pressure  of  the 


DIFFUSION  OF  GASES. 


air  within  B  has  been  increased,  and  that  gas  is  accordingly 
forced  out  through  the  tube. 

What  has  taken  place?  The  hydrogen  from  A  must 
have  passed  through  the  pores  of  B  into  the  interior.  It 
does  so  by  a  process  called  Diffusion, 
which  is  of  the  same  character  as  the 
diffusion  of  liquids  described  on  page 
179.  But  not  only  has  the  hydrogen  gas 
diffused  through  the  pores  of  the  jar 
into  its  interior,  but  some  of  the  air  from 
within  has  diffused  outward  at  the  same 
time.  The  hydrogen,  however,  goes  in 
faster  than  the  air  comes  out.  When  B 
was  standing  in  the  air  before  the  ex- 
periment, diffusion  of  the  outside  air 
.into  the  interior,  and  of  the  inside  air 
outward,  was  similarly  taking  place.  We 
did  not  observe  it,  because  the  diffusion 
each  way  was  at  the  same  rate,  the  gas 
being  the  same,  and  at  the  same  tempera- 
ture, inside  and  out.  Thus  hydrogen  and  air  diffuse  at 
different  rates. 

EXPERIMENTS. — Remove  the  jar  A  immediately  after  the  experi- 
ment above.  The  liquid  of  D  will  rise  in  the  tube,  for  there  is  now 
only  air  outside  B,  while  inside  there  is  a  mixture  of  hydrogen  with 
air.  This  mixture  diffuses  outward  faster  than  the  air  diffuses  inward. 

After  all  the  hydrogen  has  escaped  from  B,  fill  A  with  carbonic- 
acid  gas.  This  is  heavier  than  air,  and  will  escape  when  A  is  inverted, 
unless  the  mouth  of  the  jar  is  kept  closed  with  a  cardboard.  Invert 
A  over  B.  The  liquid  will  now  be  seen  to  rise  in  C.  The  carbonic- 
acid  gas  diffuses  more  slowly  than  air. 

Gases  are  thus  shown  to  diffuse  through  porous  parti- 
tions. In  general,  the  less  dense  gases— e.  g.,  hydrogen — 
diffuse  faster  than  the  more  dense  ones,  as  carbonic  acid. 

Free  Diffusion. — Gases  also  diffuse  into  each  other 
when  merely  in  contact,  and  not  separated  by  porous  par- 


FIQ.  119. 


222  LIQUIDS  AND  GASES. 

titions ;  this  can  not  be  as  conveniently  shown  experiment- 
ally, but  may  in  a  measure  be  illustrated  thus : 

Pour  a  little  strong  ammonia-water  into  a  shallow  dish  in  a  small 
closed  room.  A  smell  of  ammonia  will  soon  be  perceived  throughout 
the  apartment.  This  illustrates  the  free  diffusion  of  gases,  as  ammo- 
nia is  a  gas,  ammonia-water  being  a  solution  of  this  gas  in  water. 
When  the  solution  stands  open,  some  of  the  gas  passes  off  into  the 
air  and  quickly  diffuses  through  the  room.  Most  odors  are  gases  or 
vapors  diffusing  in  this  way. 

The  diffusion  of  one  gas  into  another  is  similar  in  nature 
to  liquid  diffusion.  The  molecules  of  each  gas,  in  their  free 
movement,  pass  off  into  the  spaces  between  the  molecules  of 
the  other  gas.  Why  do  the  less  dense  gases  diffuse  faster  ? 
Equal  volumes  of  all  gases  contain  the  same  or  nearly  the 
same  number  of  molecules.  Hence  the  molecules  of  the 
less  dense  gases  have  the  less  mass.  At  the  same  temperature, 
the  less  massive  molecules  move  faster  than  the  more  mas- 
sive ones,  and  therefore  penetrate  farther  in  the  same  time. 

Diffusion  through  Membranes. — Fill  a  small  bottle 
having  a  large  mouth  with  hydrogen,  and  tie  over  it  a  piece 
of  softened  bladder.  The  bladder  will  at  once  begin  to  be 
drawn,  or  rather  pressed,  inward  in  a  concave  form.  The 
hydrogen  diffuses  outward  faster  than  the  air  passes  in, 
leaving  a  partial  vacuum. 

Fill  the  bottle  with  carbonic-acid  gas  instead  of  hydrogen.  Fill  a 
larger  inverted  bottle  with  hydrogen  and  hold  it  down  over  the  bottle 
of  carbonic  acid.  The  bladder  will  bulge  outward,  for  the  hydrogen 
diffuses  inward  faster  than  the  carbonic  acid  outward,  thus  making 
the  pressure  inside  greater  than  that  outside. 

These  experiments  show  that  gases  possess,  like  liquids, 
the  property  of  Osmosis,  or  diffusion  through  membranes. 


THE  EARTH'S  ATMOSPHERE. 

The  Atmosphere  consists  of  an  immense  mass  of  invis- 
ible elastic  fluid,  which  we  call  air,  completely  surrounding 


THE  ATMOSPHERE.  223 

the  earth,  and  held  in  place  by  its  own  weight.  It  consists 
chiefly  of  four  volumes  of  nitrogen  and  one  of  oxygen,  but 
also  contains  less  than  one  per  cent  of  vapor  of  water  and.  a 
small  amount  of  carbonic  acid.  Owing  to  free  diffusion  and 
to  the  stirring  action  of  winds,  the  atmosphere  is  a  thorough 
mixture  of  these  gases,  the  proportions,  except  of  aqueous 
vapor,  being  everywhere  almost  exactly  the  same,  except  in 
confined  spaces,  such  as  buildings,  mines,  etc. 

As  this  atmosphere  is  kept  in  place  by  its  weight  only, 
the  pressure  within  it  must  be  greater  the  farther  we  descend 
into  it  from  the  outside,  just  as  the  pressure  increases  with 
the  depth  in  a  liquid.  Indeed,  the  atmosphere  has  been 
likened  to  an  ocean  of  air.  But  air  is  easily  compressible, 
and,  of  course,  the  more  it  is  under  compression  the  more 
dense  it  is.  Therefore,  if  we  were  to  descend  from  the  out- 
side into  the  earth's  atmosphere,  we  should  find  not  merely 
that  the  pressure  was  greater,  but  that  the  air  was  more  and 
more  dense  the  farther  we  descended.  Thus,  while  the 
water  pressure,  as  we  descend  into  the  ocean,  would  be  found 
to  increase  proportionally  to  the  depth,  and  the  water  to  be 
of  sensibly  uniform  density,  owing  to  its  very  slight  com- 
pressibilty — in  descending  into  the  earth's  atmosphere,  we 
should  find  the  pressure  to  increase  much  more  rapidly  than 
in  proportion  to  the  depth,  and  the  density  of  the  easily 
compressible  air  to  increase  more  rapidly  also.  In  other 
words,  if  we  were  to  ascend  from  the  surface  of  the  earth, 
we  should  find  the  air  growing  less  dense  (or  more  rarefied), 
and  the  pressure  lessening  more  rapidly  than  in  proportion 
to  the  height.  Owing  to  this  fact,  the  greater  part  of  the 
mass  of  the  atmosphere  is  near  the  earth,  one  half  of  it  be- 
ing probably  within  three  and  a  half  miles  of  the  earth's 
surface.  The  upper  air  is  extremely  rarefied,  and  shades  off, 
as  it  were,  very  gradually  into  empty  space. 

The  Depth  of  the  Atmosphere,  or  the  distance  to 
what  may  be  called  its  upper  limit,  can  not  be  accurately 


224 


LIQUIDS  AND  GASES. 


determined,  for  this  limit  is  not  well  marked ;  but  it  is  esti- 
mated to  be  between  thirty  and  sixty  miles.  It  is  probable 
that  there  are  minute  perceptible  traces  of  air  as  high  as 
several  hundred  miles  from  the  surface.  If  the  atmosphere 


7 


-2 


-1-5- 


•-10-.-2- 


•6.8 


Himalaya  Mountains  I 


FIG.  120. — DIMINUTION  IN  DENSITY  AND  PRESSURE  OF  AIR  WITH  INCREASE  OF 

HEIGHT. 

were  of  uniform  density  throughout,  the  same  as  that  at  sea- 
level,  it  would  be  sufficient  in  volume  to  cover  the  earth 
with  a  layer  only  about  five  miles  deep,  out  of  which  some 
of  the  highest  mountains  would  project. 

The  atmosphere,  or  more  properly  the  air,  does  not  stop  at  the 
earth's  surface,  but  penetrates  into  all  holes,  crevices,  and  porous  sub- 
stances, and  must  therefore  be  present  at  considerable  depths.  Its 
density  at  such  depths  may  become  very  great. 

The  Atmosphere  exerts  the  Pressure  due  to  its 
Weight  upon  all  objects  on  the  earth,  our  bodies  included. 


BUOYANCY  OF  GASES.  225 

The  total  force  thus  exerted  is  enormous,  although  we  do 
not  perceive  it. 

For  example,  the  surface  of  a  man's  body  is  about  16  square  feet, 
or  16  x  144  =  2,124  square  inches.  The  intensity  of  the  atmospheric 
pressure  is  14'7  pounds  per  square  inch.  The  total  pressure  on  the  sur- 
face of  the  body  is,  then,  2,124  x  14'7  =  31,200  pounds,  or  nearly  16 
tons.  It  might,  at  first  thought,  seem  that  this  pressure  must  crush 
us.  It  would  do  so,  were  it  applied  merely  upon  the  outside ;  but, 
through  the  air  and  liquids  contained  in  the  tissues  and  passages  of 
the  body,  this  pressure  is  rendered  the  same  in  all  directions  through- 
out the  interior  of  the  body. 

The  Measurement  of  Heights  by  the  Barometer 

depends  upon  the  vertical  diminution  of  the  atmospheric 
pressure.  If  a  barometer  be  read  at  the  foot  of  a  mountain 
and  then  at  the  summit,  the  second  reading  will  be  less 
than  the  first.  From  the  difference  in  reading,  the  law  of 
diminution  being  known,  the  height  can  be  computed. 

Owing  to  the  disturbances  of  pressure  accompanying  storms,  and 
to  irregularities  due  to  temperature  and  humidity,  barometric  indica- 
tions do  not  afford  an  exact  method  of  measuring  heights.  The 
barometer  falls  about  one  inch  for  the  first  one  thousand  feet  above 
sea-level,  but  this  rate  is  not  maintained. 

Buoyancy  of  Air. — Fig.  121  shows  a  hollow  sphere  sus- 
pended from  one  arm  of  a  balance  beneath  the  receiver  of 
an  air-pump.  Any  light  object  will  an- 
swer instead  of  the  sphere.  With  the  re- 
ceiver removed,  adjust  the  weight  on  the 
balance-arm  until  the  sphere  is  exactly 
counterpoised.  Then  put  the  receiver  in 
place  and  exhaust  the  air.  The  sphere 
will  descend,  showing  that  its  weight  has 
apparently  increased  as  compared  with 
that  on  the  other  arm  of  the  balance. 
But  no  change  has  been  made  except  the  FIG.  121.— GLOBE  UNDER 
removal  of  the  air  from  the  receiver. 

Why  has  the  sphere  appeared  to  gain  weight  I  We  have  seen  that 
any  body  immersed  in  water  appears  to  lose  weight,  or  is  buoyed  up,  by 


LIQUIDS  AND  GASES. 


an  amount  equal  to  the  weight  of  water  displaced.  Objects  in  air,  and 
in  all  fluids,  are  buoyed  up  in  precisely  the  same  way  by  an  amount  equal 
to  the  weight  displaced.  Thus,  when  the  sphere  was  counterpoised 
in  the  air,  it  was  buoyed  up  by  the  weight  of  its  volume  of  air.  All 
the  other  parts  of  the  apparatus  were  also  similarly  buoyed  up.  When 
the  air  was  removed  from  around  the  apparatus,  the  buoyancy  ceased. 
Every  part  of  the  apparatus  gained  in  apparent  weight,  then,  by  an 
amount  equal  to  the  weight  of  the  air  it  had  displaced.  But  the 
sphere,  being  larger  than  the  other  parts,  displaced  more  air,  and  there- 
fore was  more  buoyed  up.  Hence,  when  the  buoyancy  was  removed,  it 
appeared  to  gain  more  in  weight  than  the  other  parts,  and  that  side  of 
the  balance  went  down. 

In  weighing  any  object  accurately,  the  buoyancy  of  the  air  must  be 
allowed  for.  Both  the  object  and  the  weights  are,  of  course,  buoyed 
up,  and  appear  too  light.  But  generally  the  weights  are  of  brass, 
which  is  more  dense  than  most  materials,  so  that  the  object  loses  more 
in  weight  than  the  weights.  The  weight  of  a  litre  of  air  is  only  about 
one  gramme,  so  that  the  loss  of  weight  of  most  objects  is  so  small  as 
to  be  neglected  in  commercial  and  in  most  engineering  work.  As  all 

objects  everywhere  about  us  are 
buoyed  up,  and  as  we  never  go 
outside  of  the  air,  we  do  not  or- 
dinarily notice  this  buoyancy. 

The  Balloon. — The  ef- 
fect of  the  buoyancy  of  the 
atmosphere  is  easily  per- 
ceived in  its  action  on  bodies 
of  less  density  than  air. 

Fig.  122  represents  bub- 
bles blown  by  hydrogen  gas 
issuing  from  a  hydrogen 
generator.  Instead  of  hy- 
FIG.  122.— HYDROGEN  BUBBLES,  ILLUSTRAT-  drogen,  ordinary  illuminat- 

ING  PRINCIPLE  OF  BALLOON.  ing   gag  wiR    angwer   equally 

well,  a  glass  tube  or  a  clay  pipe  being  connected  with  the 
gas-jet  by  a  rubber  tube,  and  its  end  dipped  into  the  soap 
mixture  of  page  174.  The  hydrogen  is  so  much  less  dense 
than  air,  that  the  bubble,  even  including  the  weight  of  the 
film  and  hydrogen  together,  is  lighter  than  the  air  displaced. 


PRINCIPLE  OF  THE  BALLOON.  227 

It  is  therefore  buoyed  up  by  a  force  greater  than  its  own 
weight,  and,  like  a  block  of  wood  in  water,  tends  to  rise. 

The  hydrogen  bubble  is  a  miniature  Balloon,  for  a  real 
balloon  is  merely  a  bubble  whose  walls  are  of  a  very  light, 
strong  material,  such  as  silk  made  impervious  to  hydrogen. 
The  balloon  is  filled  or  inflated  with  this  "  gas,"  and  there- 
fore rises  with  the  car  and  its  load.  The  large  size  of  an 
ordinary  balloon  is  requisite  in  order  that  the  difference  in 
weight  between  the  hydrogen  contained  and  the  air  dis- 
placed shall  be  at  least  equal  to  the  weight  of  its  walls,  to- 
gether with  that  of  the  car  and  its  contents.  The  ordinary 
toy-balloon  is  a  rubber  bag  inflated  with  hydrogen  or  illu- 
minating gas.  The  gas  soon  escapes  by  diffusion  through 
the  rubber,  allowing  the  bag  to  collapse. 

On  account  of  the  buoyancy  of  air,  hydrogen  and  other  gases  less 
dense  than  air  tend  to  rise  through  it.  Hydrogen,  for  instance,  can  be 
held  in  a  jar  placed  mouth  downward,  while  it  would  rise  quickly  out 
of  a  jar  placed  mouth  upward.  It  can  be  poured  from  one  jar  into 
another  by  holding  them  both  mouth  downward  and  then  inclining 
the  one  containing  the  gas  beneath  the  mouth  of  the  other,  into  which 
the  hydrogen  will  rise,  displacing  the  air.  This  process  is  exactly  the 
opposite  of  pouring  water,  as  it  is  pouring  upward  instead  of  down- 
ward ;  but  gravity  is  in  each  case  the  source  of  energy. 

Gases  more  dense  than  air  can  be  poured  just  as  water  is.  Hot  air, 
being  less  dense  than  cold  air,  is  buoyed  up  in  cool  air  by  a  force 
greater  than  its  weight,  and  therefore  tends  to  rise.  This  gives  us  the 
draught  in  our  chimneys  as  well  as  many  of  the  currents  of  the  atmos- 
phere. Smoke  is  mainly  composed  of  particles  of  carbon  which  rise 
only  because  carried  along  by  hot  air.  Hot  air  was  also  used  instead 
of  hydrogen  in  the  earliest  forms  of  balloons,  and  is  the  means  by 
which  fire-balloons  are  made  to  rise. 


QUESTIONS.— Describe  an  experiment  to  show  the  diffusion  of  gases  through  a 
porous  partition.  Give  an  account  of  the  free  diffusion  of  gases.  How  is  it 
explained  on  the  molecular  theory  ?  Which  diffuse  faster,  the  more  or  the 
less  dense  gases  ?  Why  ?  Illustrate  the  osmosis  of  gases. 

Of  what  does  the  atmosphere  consist  ?  Draw  a  diagram  illustrating  the  variation 
of  pressure  of  the  atmosphere  with  the  height  ?  If  a  barometer  were  carried 
up  to  a  point  where  it  read  only  15  instead  of  30  inches,  how  much  of  the  mass 
of  the  atmosphere  would  be  above  it  ?  About  how  high  would  this  be  ?  What 


228  LIQUIDS  AND  GASES. 

is  said  of  the  height  of  the  atmosphere  ?  Why  do  not  the  gases  of  the  atmos- 
phere stratify,  as  oil  and  water  do,  into  layers  of  nitrogen,  oxygen,  etc. 

A  house  is  30  feet  long,  40  feet  broad,  and  30  feet  high,  with  flat  roof.  How  much 
is  the  total  atmospheric  pressure  on  its  outside  surface  »  Why  does  it  not  col- 
lapse ?  Would  it  collapse  if  the  air  were  removed  from  it  ? 

Why  do  we  suppose  that  air  exerts  a  buoyancy  ?  How  may  we  prove  it  ?  How 
is  this  allowed  for  in  weighing  ?  Why  is  it  imperceptible  in  ordinary  weighing  ? 
Why  do  bubbles  filled  with  hydrogen  rise  ?  Why  does  hot  air  go  up  the  chim- 
ney ?  Does  it  appear  to  you  that  gases  and  liquids  closely  resemble  each  other 
in  properties  ?  More  closely  than  liquids  resemble  solids  ? 


MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

State  the  principal  distinction  between  gases  and  liquids. 

If  one  end  of  a  skein  of  silk  be  placed  in  a  tumbler  of  water  and  the  other  be  al- 
lowed to  hang  over  the  side,  why  will  the  tumbler  in  time  be  emptied  ? 

Why,  in  an  ordinary  well,  does  not  the  water  rise  to  the  earth's  surface  ? 

Did  you  ever  see  locks  on  a  canal  ?  If  so,  explain  by  diagram  the  principle  on 
which  they  are  operated. 

Is  the  city  or  town  in  which  you  live  supplied  with  water  from  some  pond  or 
lake  ?  How  far  is  the  water  conveyed  in  pipes  ?  How  high  does  it  rise  in  the 
dwelling-houses  ?  Explain  the  principle  of  the  garden  fountain. 

Bore  a  hole  in  the  bottom  of  a  pail  of  water.  What  happens  ?  Bore  a  hole  in  the 
side  of  the  same  pail.  What  takes  place  ?  Bore  a  hole  in  the  bottom  of  an 
empty  pail  and  hold  it  upright  in  the  water.  What  occurs  ?  What  do  these 
three  results  prove  ? 

Why  does  water  run  into  a  leaky  boat  ? 

A  box  4  feet  deep  by  2  feet  wide  by  3  feet  long,  with  its  bottom  horizontal,  is  full 
of  water.  What  is  the  intensity  of  pressure  on  the  bottom  ?  What  is  the  total 
pressure  on  the  bottom  ?  What  is  the  average  intensity  of  pressure  on  its  side  ? 
What  the  total  pressure  ?  What  is  the  total  pressure  on  the  end  ?  What  would 
be  the  weight  of  water  contained  in  the  box  ?  If  the  box  was  closed  on  the  top 
and  a  square  tube  12  feet  high  and  O'l  inch  on  a  side  projected  vertically  from 
it  and  was  full  of  water,  what  would  be  each  of  these  pressures  ?  What  would 
be  the  total  weight  of  the  water  ?  How  is  it  possible  that  the  pressure  on  the 
bottom  of  the  box  can  be  so  much  greater  in  the  second  than  in  the  first  case 
with  so  little  more  water  ?  Where  is  the  upward  pressure  exerted  in  the  second 
case  which  counterbalances  all  the  downward  pressure  except  that  exerted 
through  the  lower  end  of  the  tube  ?  What  would  be  the  amount  of  each  of 
these  weights  and  pressures  if  mercury  were  used  instead  of  water  ? 

Will  a  minnow-bucket  even-full  of  water  weigh  more  if  a  dozen  live  minnows  are 
placed  in  it?  Why? 

How  many  cnbic  feet  of  cork  would  be  required  to  make  a  life-preserver  capable 
of  supporting  a  person  of  150  pounds  weight  ? 

Can  you  draw  a  diagram  explanatory  of  the  principle  of  the  pneumatic  ink- 
stand ? 

Why  can  you  float  better  in  salt  water  than  in  fresh  ?  In  a  lake  like  Great  Salt 
Lake  than  in  the  ocean  ?  Can  you  think  of  any  way  in  which  you  can  increase 
your  buoyancy  in  water  ?  Why  is  it  dangerous  to  struggle  and  raise  the  arms 
if  you  fall  into  the  water  and  can  not  swim  ?  What  should  be  done  under  such 
cirQuinstauces  ? 


MISCELLANEOUS  QUESTIONS.  229 

WU<1  ducks  and  geese,  whose  breasts  are  covered  with  thick  down,  float  easily  on 
water.  Think  of  a  reason. 

Why  does  a  loaded  vessel,  in  ascending  the  Mississippi  from  the  Gulf,  draw  more 
and  more  water  as  she  proceeds  ? 

Dip  the  corner  of  a  piece  of  blotting-paper  into  your  ink-stand  and  explain  what 
takes  place. 

Did  you  ever  notice  in  raising  a  filled  bucket  from  a  well  that  it  becomes  heavier 
the  moment  it  leaves  the  water  ?  Why  is  this  ? 

In  the  common  atomizer  used  for  spraying  the  throat,  why  does  squeezing  the 
rubber- bulb  force  into  the  air  fine  drops  of  the  solution  contained  in  the  bottle  ? 
Explain  the  double  action. 

How  high  does  water  rise  in  a  boat's  "  well  "  ? 

Why  does  the  body  of  a  drowned  person  sink,  but  after  a  few  days,  if  the  water 
is  comparatively  shallow,  rise  to  the  surface  ?  When  water  is  breathed  into 
the  lungs,  the  specific  gravity  of  the  body  is  increased  and  causes  it  to  sink. 
After  remaining  under  water  for  a  time,  light  gases  are  generated  within  the 
body,  distending  it,  and  thus  lessening  its  specific  gravity,  so  that  it  floats. 
Can  a  lake  be  so  deep  that  the  body  of  a  person  drowned  in  it  will  not  rise  ? 

The  centrifugal  tendency  in  the  gyratory  motion  of  a  tornado  is  tremendous,  and 
the  diminution  of  atmospheric  pressure  at  the  center  is  such  as  to  create  a  par- 
tial vacuum.  Explain  then  why,  when  a  tornado  passes  over  a  building,  the 
structure  may  burst  into  fragments. 

It  is  desired  to  know  whether  a  supposed  silver  piece  is  pure.  Its  weight  in  air  is 
found  to  be  16'8  grammes,  in  water  14'8  grammes.  Is  it  probably  silver  ? 

A  bottle  empty  weighs  35  grammes  ;  full  of  water,  65  grammes  ;  full  of  another 
liquid,  75'8  grammes.  What  is  the  density  of  the  liquid  ?  What  is  the  liquid  ? 

Into  what  space  must  we  compress  10  cubic  inches  of  air  to  double  its  elastic 
force  ? 

What  is  the  weight  of  600  cubic  inches  of  air  ?  What  is  the  weight  of  the  same 
bulk  of  water  ? 

A  vessel  full  of  air  weighs  1,061  grains ;  exhausted,  it  weighs  but  1,000  grains. 
How  many  cubic  inches  does  it  contain  ? 

What  amount  of  atmospheric  pressure  is  supported  by  a  boy  whose  body  con- 
tains 1,000  square  inches  of  surface  ? 

WTien  the  mercury  in  the  barometer  stands  at  29  inches,  at  what  height  will  a 
column  of  water  be  supported  by  the  atmosphere  ? 

When  the  atmosphere  supports  a  column  of  water  32  feet  high,  how  high  a  col- 
umn of  mercury  will  it  support  ? 

How  far  above  the  earth's  surface  would  the  mercury  stand  only  two  inches  high 
in  the  barometer  ? 

Does  the  air  stop  at  the  earth's  surface  ?  What  must  be  its  density  in  deep 
mines  ? 

How  many  cubic  feet  of  air  would  it  take  to  weigh  as  much  as  4  cubic  feet  of 
water  ?  Ans.  3.3334  cubic  feet. 

How  much  would  a  cubic  foot  of  gold  weigh  ?    How  much,  one  of  silver  ? 

What  would  be  the  weight  of  4  cubic  feet  of  marble  ? 

Suppose  a  room  10  feet  high,  long,  and  wide,  to  be  filled  with  gold,  what  would 
the  gold  weigh  ?  Ans.  1,212,500 pounds. 

If  a  balloon  with  car  loaded  weighs  500  pounds,  how  big  must  it  be,  if  filled  with 
hydrogen,  just  to  carry  this  load  ? 


HEAT. 

NATURE  OF  HEAT. 

Heat  is  a  Form  of  Energy  possessed  by  bodies  in 
virtue  of  an  irregular  motion  of  their  molecules,  as  described 
on  page  37.  It  addresses  the  sense  of  touch.  Its  nature  is 
imperfectly  understood.  We  consciously  perceive  it  when 
it  is  communicated  from  anything  hot  to  our  persons,  but 
we  can  not  explain  what  it  is. 

Heat  neither  increases  nor  diminishes  the  weight  of  bod- 
ies. An  iron  ball  when  cold  is  exactly  as  heavy  as  it  is  when 
heated  red-hot. 


NOTE.— With  the  simple  apparatus  shown  above  most  of  the  experiments  de- 
scribed in  the  following  section  on  Heat  may  be  performed  :  No.  1  represents  an 
iron  support,  with  sliding  rings ;  2,  a  glass  beaker ;  3,  a  cylindrical  bulb  ther- 
mometer ;  4,  a  glass  funnel ;  5,  a  test-tube  stand  with  tubes  ;  6,  a  Bunsen  burner, 
with  regulator  for  the  air,  intended  to  be  connected  with  a  gas-jet  by  a  length  of 
rubber  tubing  ;  7,  a  pulse  glass  ;  8,  a  glass  retort ;  9,  a  U-shaped  tube  ;  10,  a  con- 
denser ;  11,  a  glass  balloon,  with  stop-cock,  for  weighing  gases  ;  12,  a  metal  tri- 
pod ;  13,  a  glass  flask  ;  14,  a  glass  air-thermometer ;  15,  an  aspirator  bottle  lor 
siphon  ;  16,  a  standard  balance  ;  17,  a  retort  receiver  ;  18.  a  spirit-lamp,  which 
must  be  substituted  for  the  Bunseu  burner  when  illuminating  gas  is  not  access- 
ible. A  few  perforated  rubber  corks  of  different  sizes  should  also  be  procured,  a 


TEMPERATURE.  231 

When  heat  is  communicated  to  a  bod}7,  the  body  is  not 
necessarily  perceptibly  warmed.  If  heat  be  communicated 
to  a  substance  and  does  not  perceptibly  warm  it  (as  when 
a  tumbler  of  hot  water  is  poured  into  a  pitcher  of  broken 
ice),  such  heat  is  said  to  have  been  "rendered  Latent " — 
in  reality,  it  has  been  changed  into  other  forms  of  energy, 
sometimes  partly,  sometimes  wholly,  outside  the  substance 
in  question. 

Temperature. — When  a  body  feels  hot  or  cold,  we  may 
express  the  fact  by  saying  that  its  Temperature  is  higher 
or  lower  than  that  of  the  hand.  We  can  not  always  judge 
correctly  of  the  temperature  of  a  body  by  our  sense  of  touch. 
If,  for  instance,  an  iron  rod  and  a  piece  of  wood  be  exposed 
for  several  hours  in  a  hot  oven,  the  iron  will  feel  much 
hotter  than  the  wo'od.  The  iron  may  even  blister  the  hand, 
while  the  wood  can  be  held  without  inconvenience. 

Similarly,  in  arctic  regions,  very  cold  iron  will  blister,  so  that  the 
iron-work  of  vessels  is  covered  with  badly  conducting  material  (see 
page  276)  to  prevent  the  cold  metal  from  coming  in  contact  with  the 
hand.  Wood  and  cloth  at  the  same  low  temperature  do  not  feel  cold. 
This  is  because  the  hot  iron  parts  with  its  heat  more  readily  than  the 
wood  or  cloth,  while  the  cold  iron  removes  the  heat  more  rapdily  from 
the  hand.  A  similar  fact  is  observed  in  the  case  of  oil-cloth  and  car- 
pets at  the  same  temperature. 

glass  stirring  rod,  some  rubber  tubing,  and  a  pound  of  assorted  glass  tubing, 
which  may  be  cut  with  a  wet  three-cornered  file,  or  softened  in  the  alcohol  or 
Bunsen  flame,  and  drawn  into  any  desired  shape.  It  is  advisable  always  to  pro- 
tect a  glass  retort  from  the  Bunsen  flame  by  a  square  of  fine  wire  gauze.  The 
teacher  or  pupil  will  be  supplied  with  this  outfit,  at  a  moderate  price,  by  any 
manufacturer  of  philosophical  apparatus.  Where  economy  is  necessary,  a  suffi- 
ciently accurate  balance  may  be  made  with  a  cross-bar  of  hard  wood  and  scale- 
pans  cut  out  of  tin.  A  glass  bottle  divided  in  halves  furnishes  at  once  a  beaker  B 
and  a  funnel  F.  Prof.  Woodhull,  in  his  "Home-Made  Apparatus," 
suggests  that  a  deep  incision  be  filed  in  the  side  of  the  bottle,  and  a 
hot  poker  be  drawn  from  the  incision  round  the  bottle  in  the  required 
direction.  A  crack  will  start  at  the  incision,  and  follow  the  poker  till 
the  bottle  is  divided.  K  a  piece  of  yarn  saturated  with  kerosene  be 


wound  twice  round  a  common  beer-bottle  and  lighted,  and  the  whole    „ 

be  then  plunged  into  cold  water,  the  bottle  will  separate  as  shown  in 

the  cut.    Holes  may  also  be  bored  in  glass  vessels  by  means  of  a  broken-off 

round  file,  and  glass  tubes  fitted  therein  with  the  aid  of  rubber  corks  or  tubing. 


232  HEAT. 


EFFECTS  OF  HEAT. 

When  Heat  is  applied  to  a  Body,  the  effect  pro- 
duced varies  with  the  nature  of  the  body.  Heat  may  cause 
a  rise  of  temperature,  or,  as  we  ordinarily  say,  the  body  may 
become  warmer.  If  the  body  is  solid,  it  may  fuse  or  liquefy 
when  heat  is  applied  ;  and  liquids  may  be  vaporized  by  a 
continued  addition  of  heat.  Some  bodies,  like  wood,  do  not 
fuse,  but  decompose  into  constituent  compounds  or  ele- 
ments ;  others,  like  paraffine,  decompose  after  fusion,  but 
before  vaporization  proper  sets  in.  Heating  a  body  also 
causes  a  change  in  its  volume.  In  most  cases,  bodies  ex- 
pand when  heated. 

Conversely,  if  heat  be  removed  from  bodies,  the  changes  above 
named  generally  take  place  in  the  reverse  order.  Vapors  condense 
into  liquids,  liquids  solidify,  and  the  temperature  of  bodies  falls.  If 
heating  a  body  causes  it  to  expand,  cooling  will  cause  it  to  contract, 
and  vice  versa.  But  the  decomposition  of  bodies  effected  by  heat  is 
not  capable  of  being  reversed  by  a  simple  process  of  cooling. 

Rise  of  Temperature  produced  by  Heat. — If  a  ves- 
sel of  iced  water  be  placed  upon  a  stove,  the  water  becomes 
warmer,  and  soon  begins  to  boil.  During  this  operation, 
the  heat  obtained  at  the  expense  of  the  burning  fuel  is  being 
continuously  added  to  the  vessel  of  water.  The  vessel  may 
be  removed  to  a  cold  room,  where  it  will  serve  as  a  source  of 
heat ;  for,  as  it  cools,  it  imparts  the  heat  which  it  has  re- 
ceived to  the  room.  One  system  of  heating  buildings  is  by 
the  cooling  of  hot  water  conveyed  in  pipes. 

If  the  vessel  be  placed  in  an  ice-box,  where  it  is  entirely 
surrounded  by  ice,  it  will  cool  down  to  the  temperature  of 
the  ice.  During  this  operation,  the  hot  water  parts  with 
heat,  which  melts  a  portion  of  the  ice.  The  vessel  of  cold 
water  might  now  be  used  to  cool  a  hot  room,  just  as  the  hot 
vessel  was  used  as  a  source  of  heat.  This  principle  is  ap- 
plied to  the  cooling  of  railroad  cars,  etc.,  in  hot  countries. 


EXPANSION  OF  SOLIDS. 


233 


During  the  coldest  mornings  in  winter,  a  piece  of  ice  lying  on  the 
ground  may  be  much  colder  than  another  piece  which  has  just  formed 
by  solidification.  If  heat  be  applied  to  the  former,  it  will  not  at  once 
fuse,  but  will  first  become  warmer ;  and  this  operation,  like  those  pre- 
viously described,  will  require  time.  The  ice  behaves  like  lead  or  iron 
which  have  cooled  below  the  temperatures  at  which  they  fuse.  The 
difference  in  these  cases  is  that  lead  must  be  made  much  warmer  than 
ice,  and  iron  still  warmer  than  lead,  before  fusion  will  take  place. 

Expansion  of  Solid  Bodies  by  Heat. — The  expansion 
of  a  solid  may  be  illustrated  by  means  of  an  apparatus  like 
that  shown  in  Fig.  125. 

Provide  yourself  with  an  iron  ball  or  grape-shot,  to  which  a  black- 
smith will  attach  a  metal  hook,  so  that  you  can  manage  it  when  hot. 
Then  have  constructed  an  iron  ring  just  large  enough  to  let  the  ball 
pass  through  when  they  have  the  same  temperature.  If  the  ball  alone 
is  heated  in  the  flame  of  a  spirit-lamp  or  Bunsen  burner,  it  will  expand 


FIG.  125.— EXPANSION  ILLUSTRATED. 

to  such  a  degree  that  it  can  not  pass  through  the  ring.  If  the  ring 
alone  is  heated,  it  will  be  too  large  to  fit  the  ball  closely,  and  the  ball 
can  be  made  to  rattle  against  its  interior  rim.  If  both  are  heated  or 
cooled  alike,  the  ball  will  always  fit  the  rim.  On  this  principle,  the 
blacksmith  heats  the  iron  tire  before  applying  it  to  the  wooden  wheel. 

If  a  bar  of  metal  is  heated,  it  elongates.     In  a  railroad 
track,  the  rails  are  always  left  with  a  little  space  between 
their  ends,  in  order  to  allow  for  expansion.     Conversely, 
16 


234 


HEAT. 


when  iron  cools,  it  contracts.  The  tie-rods  of  bridges  expand 
and  contract  under  the  influence  of  extreme  heat  and  cold, 
sometimes  to  such  an  extent  as  to  endanger  the  structures. 

Expansion  of  Liquids  and  Gases. — To  illustrate  the 
expansion  of  liquids,  secure  a  large  glass  bulb  with  a  capil- 
lary stem  (see  Fig.  126).  Insert  the  open  end  of  the  stem 
in  water,  and  warm  the  bulb  by  the  hand  or  with  hot  water. 
The  air  will  expand,  and  part  of  it  will  be  expelled.  As  the 
bulb  cools,  the  air  within  will  contract,  and  some  water  will 
enter  through  the  capillary  stem.  The 
bulb  may  then  be  placed  in  an  upright 
position,  and  the  water  'within  boiled,  care 
being  taken  to  keep  the  whole  interior 
of  the  bulb  wet,  in  order  to  prevent  break- 
age. If  the  bulb  be  again  inverted  and 
the  end  of  the  stem  plunged  under  water, 
the  bulb  will  gradually  fill  as  it  cools. 
Why  ?  In  filling  a  bulb  with  alcohol  or 
ether,  the  source  of  heat  should  be  hot 
water,  and  not  a  flame,  in  order  to  avoid 
explosions. 

By  repetitions  of  the  operation  just  described, 
the  bulb  and  a  portion  of  the  stem  are  filled 
with  liquid  (see  Fig.  126).  If  the  bulb  be  now 
placed  in  hot  water,  or  in  melting  snow  or  ice, 
the  expansion  or  contraction  of  the  liquid  with- 
in will  be  indicated  by  its  rise  or  fall  in  the 
tube.  The  amount  of  this  rise  or  fall  will  be  greater,  as  the  volume 
of  the  bulb  is  greater,  or  the  bore  of  the  tube  is  less.  Doubling  the 
volume  of  the  bulb  will  make  the  rise  twice  as  great,  although  a 
longer  time  will  be  required  to  heat  the  bulb  throughout.  Reducing 
the  bore  of  the  tube  one  half  will  also  make  the  rise  twice  as  great, 
without  increasing  the  time  required  by  the  bulb  to  respond  to  a 
change  in  temperature. 

The  Expansion  of  Air  may  be  illustrated  with  the 
same  apparatus  by  introducing  into  the  stem  a  small  globule 


FIG.  126.— BULB-TUBES. 


THE  THERMOMETER.  235 

of  mercury  as  an  index,  the  bulb  being  filled  with  air.  The 
heat  of  the  hand  is  sufficient  to  send  the  index  through  the 
entire  length  of  the  tube,  which  should  be  in  a  horizontal 
position.  Such  bulb-tubes  are  called  Thermoscopes. 

QUESTIONS.— What  is  Heat  ?  Outline  the  accepted  theory.  When  heat  has  been 
communicated  to  a  body  and  does  not  perceptibly  warm  it,  what  has  taken 
place  ?  Illustrate  your  answer.  What  is  such  heat  sometimes  called  ?  Which 
of  the  senses  does  heat  address  ?  How  does  heat  affect  the  weight  of  bodies  ? 

What  is  the  Temperature  of  a  body  ?  Can  we  judge  of  a  body's  temperature  by 
the  sensation  it  produces  when  we  touch  it  ?  Advance  facts  to  prove  your 
answer.  What  phenomena  are  observed  in  arctic  regions  ? 

State  the  several  effects  of  heat ;  of  cold.  Explain  the  prin- 
ciple on  which  the  heat  of  burning  fuel  causes  a  rise  of 
temperature  in  water  ;  the  principle  on  which  heat  applied 
to  ice  may  not  at  once  melt  it.  Show  that  metals  fuse  in 
accordance  with  the  same  law.  Can  you  suggest  an  experi- 
ment by  which  the  expansion  of  solids  by  heat  may  be 
illustrated  ?  Experiments  showing  the  expansion  of  liquids 
and  gases  ?  What  is  indicated  by  the  Thermoscope  ? 


THERMOMETERS    AND    .THERMOMETER- 
SCALES. 

The  Thermometer,  as  usually  construct- 
ed, consists  of  a  spherical  or  cylindrical  glass 
bulb,  provided  with  a  stem  having  a  fine  capil- 
lary tube.  The  bulb  and  a  part  of  the  stem 
are  filled  with  some  liquid,  which  is  then  boiled 
to  expel  all  the  air,  and  the  tube  is  sealed  up. 
Thermometers  intended  to  be  used  at  very 
low  temperatures  are  usually  filled  with  al- 
cohol, while  those  designed  for  ordinary  or 
higher  temperatures  contain  mercury.  The 
air  thermometer,  already  described,  is  still 
used.  It  was  employed  to  measure  differ- 
ences in  temperature  as  early  as  the  sixteenth 
century,  Galileo's  first  thermometer  being  con- 
structed on  this  principle. 

Thermometer-Scales The  scale  of  the  FlG-  ™r-<*™- 

DRICAL      BULB 

thermometer  is   established  by  inserting  the      THERMOMETER. 


236 


HEAT. 


bulb  in  melting  ice,  and  in  steam  from  water  boiling  under  the 
average  pressure  of  the  air  at  sea-level.  The  temperatures  of 
ice  and  steam  under  these  conditions  are  found  to  be  constant. 

The  temperature  of  melting  ice  is  marked  32°  on  the  Fahrenheit 
scale  and  0°  on  the  Centigrade  and  Reaumur  scales.  The  tempera- 
ture of  boiling  water  at  the  sea-level  is  marked  212°  on  the  Fahren- 
heit scale,  100°  on  the  Centigrade,  and  80°  on  the  Reaumur.  The 
interval  between  the  freezing  and  boiling  temperature  of  water  is 
therefore  100  Centigrade,  180  Fahrenheit,  and  80  Reaumur  degrees. 

One  Centigrade  degree  is  thus  equal  to  £ 
Fahrenheit  degrees.  If  a  Fahrenheit  ther- 
mometer reads  60°,  the  temperature  is  there- 
fore 60  —  32  =  28  Fahrenheit  degrees  above 
the  freezing-point.  But  28°  F  =  f  28°  C,  or 
15°'5  C  ;  hence  if  C  be  the  reading  of  a  Centi- 
grade thermometer  and  F  that  of  a  Fahrenheit 
at  the  same  temperature, 

C  =  |  (F  -  32) 


80 


100 


212 


o  |r.a?i 

FIG.  128.-SCALES  COM-       That  ^  tQ  reduce  ft  Fahrenheit  to  a  Centigrade 
temperature,  subtract  32  and  multiply  the  re- 
mainder by  f.     To  reduce  a  Centigrade  to  a  Fahrenheit  temperature, 
multiply  by  £  and  add  32. 

Thermometers  used  in  physical  experiments  are  usually  provided 
with  a  cylindrical  bulb,  as  shown  in  Fig.  127.  In  this  form,  they  are 
both  more  sensitive  and  more  convenient. 

Maximum  and  Minimum  Thermometers. — Other 
forms  of  thermometers  are  the  maximum  and  minimum 
thermometers.  As  constructed 'for  meteorological  purposes 
they  are  shown  in  Fig.  129. 

The  maximum  thermometer  is  like  an  ordinary  mercury 
thermometer,  except  that  the  capillary  tube  has  a  narrow 
place  near  the  bulb,  through  which  the  mercury  is  forced 
as  the  temperature  rises.  When  the  temperature  falls,  the 
mercury  in  the  tube  remains  in  position,  showing  the  high- 
est temperature  reached. 

The  mercury  is  forced  back  into  the  bulb  by  whirling  the  ther- 
mometer on  a  pivot  which  pierces  the  metal  frame  near  the  top  of  the 


MAXIMUM  AND  MINIMUM   THERMOMETERS.      237 

scale.    The  lower  instrument  of  Fig.  129  represents  a  maximum  ther- 
mometer. 

The  minimum  thermometer  usually  has  alcohol  as  a 
liquid.  The  tube  is  of  rather  large  bore;  within  it  is  a 
small  glass  rod  below  the  surface  of  the  alcohol.  When  the 


FIG.  129.— SET  OF  MAXIMUM  AND  MINIMUM  THERMOMETERS.    (LATEST  U.  S.  SIGNAL 
SERVICE  PATTERN.) 

temperature  falls  and  the  surface  sinks,  the  glass  rod  is 
forced  along  by  the  liquid  and  does  not  break  through  the 
film  which  bounds  the  surface  of  the  alcohol.  When  the 
temperature  rises  again,  the  alcohol  flows  past  the  index, 
leaving  it  marking  the  lowest  temperature  reached. 

The  maximum  thermometer  records  the  highest  temperature  of 
the  day;  the  minimum,  the  coldest  temperature  of  the  night.  The 
mean  of  these  temperatures  is  almost  exactly  the  average  temperature 
of  the  entire  day.  When  in  use,  these  thermometers  are  placed  in  a 
horizontal  position. 

LAW  OF  EXPANSION. 

The  Coefficient  of  Linear  Expansion With  the  aid 

of  the  thermometer,  the  law  of  expansion  of  bodies  can  be 
examined.  If  a  bar  of  iron  be  compared  at  different  tem- 
peratures with  a  standard  bar  at  a  fixed  temperature,  it  is 
found  that  the  elongation  of  the  bar  per  foot,  per  degree  of 
temperature,  is  very  nearly  uniform  at  all  ordinary  temper- 
atures. If  this  quantity  be  called  a,  the  elongation  of  I  feet 
for  one  degree  would  be  I  times  as  great,  or  la.  If  the 
elongation  for  /  feet  heated  through  one  degree  is  la,  for  t° 


238  HEAT. 

the  elongation  would  be  alt.     The  final  length  I'  would  be 
the  original  length  Z,  plus  the  elongation  atl,  or 
V  =  I  +  all 

The  quantity  a  is  called  the  Coefficient  of  Expansion. 

The  coefficients  of  expansion  for  the  Centigrade  degree 
of  eight  different  metals  are  given  in  the  following  table : 

White  glass  ....  0'0000086  Copper  .       .       .       .       .  0-0000172 

Untempered  steel        .        .  O'OOOOIOS  Silver     .        .        .        .        .  0-0000191 

Cast  iron        ....  O'OOOOllS  Tin O'OOOOSl? 

Wrought  iron        .        .        .  0-0000122  Lead 0'0000286 

Tempered  steel    .        .        .  0'0000124  Zinc        .        .        .        ...  0'0000294 

A  tempered  steel  bar  one  foot  long,  when  heated  one  degree  centi- 
grade, will  become  1-0000124  feet  in  length.  If  one  mile  long,  it 
would  become  1-0000124  miles,  the  increase  in  length  in  the  latter 
case  being  0-0654  feet.  When  heated  from  0°  C.  to  20°  C.,  the  mile 
bar  would  be  increased  in  length  1-3089  feet. 

As  the  Fahrenheit  degree  is  only  f  as  long  as  the  Centi- 
grade, the  coefficients  of  expansion  for  the  Fahrenheit  de- 
gree would  be  %  of  those  given  above. 

Temperature    Compensation.  —  The 

coefficients  of  expansion  of  different  sub- 
stances being  known,  it  is  easy  to  arrange  a 
system  of  rods  which  shall  be  compensated 
for  changes  in  temperature. 

Let  S  B  (Fig.  130)  be  a  glass  rod  40  inches  in 
length  suspended  at  S  and  having  a  washer  B 
cemented  to  its  lower  extremity.  B  N  is  a  per- 
forated cylinder  of  zinc  slipped  on  over  the  rod  and 
resting  upon  the  washer.  What  must  be  the  length 
B  N  of  the  zinc  cylinder  in  order  that  its  upper 
end  shall  always  remain  at  a  fixed  distance  from 
S  when  both  rod  and  cylinder  are  equally  heated 

or  cooled?     This  problem  may  be  solved  by  sim- 

,.          i     ,    •,  i       T_          ij         £  i      FIG.  130. — COBIPEN- 

ple  proportion ;  but  it  may  also  be  stated  as  fol-     SATED  p^^^ 

lows : 

The  elongation  of  the  glass  rod  downward,  when  heated  any  number  of 
degrees  t,  will  be  0-0000086  x  40  x  t  inches.  The  zinc  cylinder  having  a  length  I, 
when  heated  an  equal  number  of  degrees,  will  elongate  upward  0*0000294  x  I  x  t 


CUBICAL  EXPANSION. 


239 


inches.  These  elongations  are  to  be  equal,  or  8613  x  40  x  t  =  29417  x  I  x  t.  Since  t 
may  be  cancelled  from  the  equation,  we  have  /  =  ~5X£fy~  =  11*7  inches. 

By  such  means  pendulums  are  compensated,  so  that  their  lengths 
remain  constant  for  varying  temperatures. 

The  expansion  thus  far  treated  is  the  expansion  of  the 
linear  dimensions  of  bodies,  and  the  coefficients  given  in  the 
table  are  called  coefficients  of  linear  expansion.  It  now  be- 
comes possible  to  determine  the  effect  of  expansion  upon  the 
volume  of  a  body.  This  increase  in  volume  is  called 

Cubical  Expansion. — A  cube  of  cast  iron  whose  edges 
are  one  foot  in  length,  when  heated  1°  C.,  would  become 
slightly  larger.  The  length  of  each  edge  would  be  increased 
by  0-00001125  feet.  The  cube  would  then  be  one  having 
edges  1-00001125  feet  in  length. 

The  expanded  cube  might  be  conceived  to  be  made  up  from  the 
smaller  one  by  placing  three  thin  blocks  upon  three  of  the  faces,  as  is 
shown  in  Fig.  131,  where  the  thickness  of  the  blocks  is  magnified 

10,000  times.    The  thickness  of  each          

block  being  0-00001125  feet,  and  the 
other  edges  being  one  foot  in  length, 
the  volume  of  each  slice  1  x  1  x 
0-00001125  =  0-00001125  cubic  feet. 
The  volume  of  the  three  slices  is  then 
0-00003375  cubic  feet.  In  order  to 
complete  the  cube,  we  need  three 
slender  rectangular  blocks  laid  along 
the  edges  shown  in  the  figure,  and  a 
little  cubical  block  in  the  corner. 
The  three  blocks  will  each  have  a  vol- 
ume of  0-00001125  x  0-00001125  x  1,  or 

0-000000000126  cubic  feet,  so  that  the  three  will  have  a  volume  of 
0  000000000378  cubic  feet.  The  volume  of  the  little  cube  required  to 
fill  out  the  corner  will  be  0-00001125x0-00001125x0-00001125,  or 
0-00000000000000142.  Adding  these  three  quantities,  the  volume  of 
the  expanded  block  will  be — 


FIG.  131.— EXPANSION  OF  IRON  CUBE. 


Original  block  . 
Three  slices      . 
Three  edge  blocks 
Corner  cube 


0-00003375 

0-000000000378 

0-00000000000000142 


240  HEAT. 

It  is  evident  that  the  two  volumes  last  written  are  too  small  to 
merit  any  consideration  in  comparison  with  the  preceding  one,  which 
is  itself  insignificant  when  compared  with  the  original  volume.  The 
cubic  foot  of  cast  iron  may,  then,  be  said  to  increase  to  1*00003375 
cubic  feet  when  heated  through  one  degree  C. 

Coefficient  of  Cubical  Expansion. — The  increase  in 
volume  of  the  unit  volume,  when  heated  through  one  degree, 
is  called  the  coefficient  of  cubical  expansion.  The  coeffi- 
cients of  cubical  expansion  of  the  substances  named  in  the 
preceding  table  may  therefore  be  obtained  by  multiplying 
their  coefficients  of  linear  expansion  by  three. 

The  coefficient  of  cubical  expansion  of  white  glass  is 
0-0000258;  that  of  mercury  is  0-000181. 
Hence,  if  a  vessel  holding  1  cubic  inch  is 
full  of  mercury  at  a  temperature  of  0°  C., 
and  is  heated  1°  C.,  the  mercury  will  ex- 
pand more  than  the  glass  by  0-000181  — 
0-000026  =  0-000155  cubic  inch.  If  glass 
expanded  more  than  mercury,  the  column 
in  a  thermometer  would  fall  when  the 
temperature  rises. 

If  a  thermometer  at  any  ordinary  tempera- 
ture be  plunged  into  warm  water,  the  column 
will  at  first  sink  and  then  rapidly  rise.  This  is 
due  to  the  fact  that  the  glass  bulb  is  heated  and 
expands  before  the  mercury  is  appreciably  affect- 
ed. If  the  thermometer  be  plunged  into  ice- 
water,  the  converse  effect  will  take  place. 

The  experiment  may  be  made  more  striking 
by  means  of  the  apparatus  shown  in  Fig.  132. 
This  consists  of  a  common  two-quart  bottle, 
filled  with  cool  water,  and  closed  by  a  stopper 
through  which  passes  a  glass  tube.  Just  above 
the  cork,  the  tube  is  drawn  out  fine.  The  up- 
per surface  of  the  water  should  be  half-way  up 
the  narrow  part  of  the  tube.  If  the  end  of  the 
FIG.  ^-BOTTLE  AND  finger  be  now  Placed  against  the  side  of  the 
GLASS  TUBE.  bottle,  the  liquid  in  the  tube  rapidly  falls,  show- 


EXPANSION  OF  WATER. 


241 


ing  that  the  glass  expanded  and  bulged  out  where  the  warm  finger 
was  applied.  The  experiments  previously  described  with  the  ther- 
mometer can  readily  be  made  with  this  apparatus. 

QUESTIONS.— What  instrument  is  used  for  measuring  changes  of  temperature  ? 
Describe  the  Thermometer  and  its  construction.  How  is  the  scale  of  the  ther- 
mometer established  ?  Name  the  three  principal  scales.  What  are  the  freez- 
ing and  the  boiling  points  respectively  called  in  the  Fahrenheit  scale  ?  What, 
in  the  Centigrade  ?  What,  in  the  Reaumur  ?  How  may  a  Fahrenheit  tempera 
ture  be  reduced  to  its  equivalent  in  centigrade  degrees  ?  A  centigrade  tem- 
perature to  its  Fahrenheit  equivalent  ? 

Describe  the  maximum  and  the  minimum  thermometer.  How  is  the  mean  tem- 
perature of  the  day  determined  ?  In  what  way  may  the  law  of  expansion  be 
studied  ?  What  is  the  coefficient  of  linear  expansion  ?  Explain  temperature 
compensation,  and  the  practical  use  that  is  made  of  coefficients  of  expansion 
in  the  construction  of  the  pendulum. 

Define  cubical  expansion,  and  show 
how  the  coefficients  of  cubical  ex- 
pansion are  obtained.  Illustrate  in 
the  case  of  a  cube  of  iron  to  which 
heat  is  applied.  In  the,  ordinary 
thermometer,  which  expands  first, 
the  glass  or  the  mercury  ?  Which 
expands  more  ?  Fully  illustrate  the 
principle.  Why  does  heating  the 
neck  of  the  bottle  uniformly  in  an 
alcohol  flame  loosen  a  tight  glass 
stopper  * 


EXPANSION   OF  WATER 
AND   GASES. 

Water    is    a    Marked 
Exception  to  the  rule  that 
bodies  are  expand- 
ed   uniformly    by 
heat.     If  water  at 
the  freezing-point 
be  warmed,  it  con- 
tracts, and  thus  be- 
comes more  dense, 
until    a   tempera- 
ture  of    4°    0      Or     FlG<  133-~ APPARATUS  FOR  DETERMINING  THE  TEMPER- 
ATURE AT  WHICH  WATER  is  DENSEST. 

39-2°  F.  is  reached, 

after  which  it  expands.     This  can  be  proved  by  means  of  the 


242  HEAT. 

bottle  of  iced  water  shown  in  Fig.  132.  If  the  apparatus  is 
placed  in  a  warm  room,  and  allowed  to  heat  slowly,  the 
column  of  liquid  will  descend  at  first  and  afterward  rise. 

The  apparatus  of  Fig.  133  has  been  used  to  determine  the  tem- 
perature at  which  water  is  most  dense.  It  consists  of  two  tubes  of 
galvanized  iron,  about  four  inches  in  diameter  and  five  feet  high.  At 
the  bottom,  the  tubes  are  connected  by  a  pipe  provided  with  a  cock,  by 
means  of  which  they  may  be  put  in  communication.  At  the  top,  they 
connect  through  an  open  trough. 

If  the  left-hand  tube  be  filled  with  water  at  0°  C.,  and  the  other 
with  water  at  8°  C.,  so  that  the  water  stands  about  a  quarter  of  an  inch 
deep  in  the  trough,  and  the  tubes  are  then  put  in  communication  at 
the  bottom,  there  will  be  no  current  in  the  trough.  If  the  water  in 
the  left-hand  tube  be  maintained  at  0°  C.  by  means  of  melting  ice,  and 
that  in  the  other  be  allowed  to  warm  a  little,  a  gentle  current  will  flow 
through  the  trough  from  right  to  left.  This  shows  that  the  water 
must  flow  through  the  lower  pipe  in  the  opposite  direction,  and  that 
the  water  at  0°  C.  exerts  a  greater  pressure  than  that  of  the  warmer 
column.  By  cooling  the  warmer  water  below  8°  C.  the  currents  are 
reversed.  In  this  way,  water  at  7°  C.  is  found  to  have  the  same  density 
as  at  1°,  at  6°  as  at  2°,  and  at  5°  as  at  3°. 

Phenomena  of  Freezing. — This  property  of  water 
plays  an  important  part  in  the  preservation  of  the  lives  of 
animals  inhabiting  lakes  and  ponds.  Only  extremely  shallow 
bodies  of  water  are  ever  frozen  to  the  bottom.  After  the 
temperature  of  a  pond  has  been  lowered  to  4°  C.  (39-2°  Fahr.) 
by  the  alternate  sinking  of  heavier  portions  of  water  cooled 
at  the  surface,  and  rising  of  warmer  and  lighter  particles 
from  below,  the  surface  layer,  as  it  grows  colder,  begins 
slowly  to  expand.  Hence  it  floats ;  and  finally,  when  it  is 
cooled  to  0°  C.  (32°  Fahr.),  it  crystallizes  into  ice,  while  the 
water  below  remains  at  4°  C.  On  freezing,  the  ice  expands 
still  more,  the  density  of  water  at  0°  C.  being  62*41  pounds 
to  the  cubic  foot,  while  that  of  ice  at  the  same  temperature 
is  58-05  pounds.  Ice,  therefore,  always  floats,  and  thus 
protects  the  denser  water  beneath,  and  the  fishes  and  plants 
that  inhabit  it,  from  further  reduction  of  temperature. 


EXPANSION  OF  GASES.  243 

The  pressure  exerted  by  freezing  water  is  irresistible.  It  often 
causes  damage  by  the  bursting  of  lead  and  iron  pipes,  and  injures 
buildings  and  stone-work.  The  farmer  avails  himself  of  the  expan- 
sion of  water  in  freezing  to  break  up  the  pieces  of  the  soil  which  he 
plows  into  furrows  in  the  autumn,  and  is  often  under  the  necessity  of 
resetting,  in  the  spring,  fence-posts  which  have  been  loosened  by  the 
frost.  Water  freezing  in  the  crevices  of  rocks  splits  them  into  frag- 
ments, as  evidenced  by  the  broken  stones  lying  at  the  base  of  cliffs. 
In  this  way,  the  obelisk  in  Central  Park,  New  York,  is  being  defaced. 

Expansion  of  Gases. — The  apparatus  shown  in  Fig. 
132  serves  to  illustrate  the  expansion  of  gases.  If  it  be 
filled  with  air,  and  the  end  of  the  tube  be  placed  under 
water,  the  air  will  bubble  out  when  the  bottle  is  heated. 

EXPERIMENTS. — Fill  a  bladder  with  air,  tie  its  neck,  and  place  it 
before  a  fire ;  the  heat  will  soon  expand  the  confined  air  to  such  a  de- 
gree as  to  burst  the  bladder. 

The  popping  of  grains  of  corn,  the  bursting  open  of  chestnuts 
when  roasting,  and  the  crackling  of  burning  wood,  are  caused  in  a 
measure  by  the  expan- 
sion of  the  air  within 
them.  Bottles  of  ef- 
fervescing drinks  are 
kept  in  a  cool  place  in 
summer,  lest  the  heat 
expand  the  carbonic- 
acid  gas  in  the  liquid  FlG  I^.—ILLUSTRATING  THE  EXPANSION  OF  GASES. 
and  break  the  bottles. 

Fill  a  small  tank  with  iced  water.  Keep  the  bulb  of  the  air- 
thermometer  in  the  water  until  it  has  cooled  down  to  zero,  and  then 
immerse  the  whole  tube,  and  fasten  it  in  a  horizontal  position,  as 
shown  in  Fig.  134.  The  bulb  and  tube  are  now  full  of  air.  Dip  out 
cold  water,  and  replace  it  with  warm.  Air  will  escape  on  account 
of  expansion,  and  may  be  collected  in  a  graduated  tube.  After  hav- 
ing heated  the  air  to  any  desired  temperature,  say  50°  C.,  maintain 
this  temperature  until  air  ceases  to  escape,  and  then  cool  the  water 
again  to  zero.  Water  will  enter  the  bulb  to  replace  the  expelled  air. 

Lower  the  mouth  of  the  collecting  tube  to  the  bottom  of  the  tank, 
so  as  not  to  lose  the  gas,  and  take  the  bulb-tube  out  of  the  water,  dry 
and  weigh  it.  If  the  water  in  the  stem  runs  out  as  the  warm  air 
strikes  the  bulb,  it  must  be  collected  and  weighed  with  the  bulb.  The 


244  HEAT. 

excess  of  this  weight  over  that  of  the  bulb  alone  gives  the  number  of 
grammes,  or  cubic  centimetres,  of  water  in  the  bulb,  or  the  number  of 
cubic  centimetres  of  air  expelled.  The  expelled  air,  if  cooled  down  to 
zero,  should  give  the  same  result,  by  direct  measurement. 

The  capacity  of  the  bulb  can  now  be  found  by  filling  the  bulb 
and  stem  with  water  at  zero  C.,  and  again  weighing.  If  the  empty 
bulb  weighed  5'2  grammes,  and  when  full  weighed  120'5  grammes, 
then  it  holds  115'3  grammes  of  water,  and  the  air  originally  in  the 
bulb  was  115*3  cubic  centimetres.  The  expansion  of  the  glass  is  so 
small  in  comparison  with  that  of  the  gas  that  it  may  be  neglected. 

From  these  data,  how  would  you  find  the  increase  in  vol- 
ume of  1  cubic  centimetre  of  air,  when  heated  1°  C.  ?  This 
quantity  is  called  the  coefficient  of  expansion  of  air. 

The   Coefficients   of  Expansion  of  all   Gases   are 

nearly  the  same,  under  all  pressures  and  at  all  tempera- 
tures. The  value  of  the  coefficient  is  ^  =  0-00366.  A 
cubic  foot  of  gas  at  0°  C.,  when  heated  1°,  will  become 
1  -f  0-00366  cubic  feet.  When  heated  to  tf°,  it  becomes 
1  _j_  0-00366  £  cubic  feet.  If  t  is  100°,  the  mass  of  gas 
which  would  have  1  cubic  foot  of  volume  at  0°,  would 
become  1-366.  In  like  manner,  1  cubic  inch  at  0°  would 
expand  to  1-366  cubic  inches  at  100°  0. 

If  the  Fahrenheit  degree  is  used,  the  coefficient  of  expansion  be- 
comes $  x  Y?"3  =  T5iT'  A  quantity  of  gas  heated  from  0°  to  273°  C. 
would  double  in  volume,  if  the  pressure  remained  unchanged. 

THERMAL    UNITS  AND  SPECIFIC  HEAT. 

Quantity  of  Heat. — A  Bunsen  burner  placed  under  a 
flask  containing  a  quart  of  water,  will  soon  raise  the  tem- 
perature of  the  water  to  the  boiling-point.  If  we  were  to 
attempt  to  boil  a  thousand  quarts  of  water  in  a  vessel,  by 
means  of  the  same  burner,  but  slight  effect  would  be  pro- 
duced. It  would  require  a  thousand  burners  to  bring  about 
rapidly  the  same  result.  In  this  latter  case,  the  amount  of 
gas  burned  would  be  a  thousand  times  as  great,  as  would, 
also  be  the  amount  of  heat  required. 


THE  HEAT  UNIT.  245 

Unit  Quantity  of  Heat. — The  unit  quantity  of  heat  is 
the  heat  required  to  raise  the  temperature  of  a  unit  mass  of 
water  through  1°.  The  actual  magnitude  of  the  heat  unit 
depends  upon  whether  the  unit  of  mass  be  the  pound,  ounce, 
gramme,  or  kilogramme,  and  whether  the  thermometer  be 
the  Centigrade  or  Fahrenheit.  To  heat  a  thousand  pounds 
of  water  1°  will  require  a  thousand  heat  units ;  to  heat  it 
5°,  five  thousand.  If  a  Bunsen  flame  be  applied  to  a  flask 
containing  500  grammes  of  water,  which  it  heats  through 
5°  C.  in  one  minute,  the  heat  added  to  the  water  is  2,500 
heat  units  a  minute. 

If  960  grammes  of  water  at  2°  C.  be  mixed  with  800  grammes  at 
24  C.,  there  will  result  1,760  grammes  of  water  at  a  temperature  t. 
This  temperature  will  evidently  lie  between  2°  and  24°,  and  must  be 
of  such  value  that  8QO  grammes  cooled  from  24°  to  t°  will  give  up 
enough  heat  to  heat  960  grammes  from  2°  to  t°.  The  heat  lost  by  the 
hot  water  is  therefore  800  (24— £)•  The  heat  gained  by  the  cold  water 
is  960  (t—2).  These  values  must  be  equal ;  or  800  (24—0  =  960  (t—2). 
Hence  t  =  12. 

If  equal  quantities  of  hot  and  cold  water  be  mixed,  the 
resulting  temperature  will  be  the  mean  of  the  hot  and  cold 
temperatures.  If  the  hot  water  be  twice  the  amount  of  the 
cold,  its  change  in  temperature  in  reaching  the  temperature 
of  the  mixture  will  be  half  that  of  the  cold  water. 

PROBLEM.— Suppose  x  grammes  of  water  at  a  temperature  of  75°  to  be  mixed 
with  40  grammes  of  water  at  3°.  The  temperature  of  the  mixture  is  15°.  Find 
the  value  of  x.  The  x  grammes  in  cooling  from  75°  to  15°  loses  (75  — 15)  x  =  60  x 
heat  units.  The  40  grammes  in  heating  from  3°  to  15°  requires  40  (15  — 3)  =  480 
heat  units.  Hence  60  x  =  480,  and  x  =  8. 

PROBLEM.— If  100  grammes  of  water  at  100°  be  put  into  500  grammes  of  cool 
water  at  10°,  the  resulting  temperature  will  be  t,  the  condition  being  100  (100  —  t) 
=  500  (£  — 10)  or  *  =  25. 

The  100  grammes  of  hot  water  cools  down  from  100°  to  25°,  yielding  7,500 
heat  units.  The  500  grammes  heats  from  10°  to  25°,  requiring  7,500  heat  units. 

If,  however,  100  grammes  of  lead  at  100°  be  mixed  with 
500  grammes  of  water  at  10°,  the  resulting  temperature  will 
be  found  to  be  10-56°. 

The  500  grammes  of  water  was  heated  only  0-56°,  requiring  500  x 
0-56  =  280  heat  units;  hence  100  grammes  of  lead  cooling  from  100° 


246 


HEAT. 


to  10-56°  =  89*44°,  yields  only  280  heat  units,  or  1  gramme  cooling  1° 
would  yield  280  -•-  (89-44  x  100)  =  0-0313  heat  units. 

Specific  Heat.  —  The  ratio  obtained  by  dividing  the 
amount  of  heat  required  to  warm  a  given  mass  of  any  sub- 
stance one  degree  by  the  amount  required  to  heat  an  equal 
mass  of  water  one  degree,  is  called  the  Specific  Heat  of  that 

substance.   Thus  the  specific  heat  of  lead  is  —      -  =  0-0313, 

I'UUUU 


the  specific  heat  of  water  being  reckoned  as  1. 

It  is  therefore  evident  that  the  specific  heat  is  numerically 
equal  to  the  quantity  of  heat  required  to  raise  the  tempera- 
ture of  a  unit  mass  of  a  given  substance  one  degree.  It 
must  be  understood,  however,  that  specific  heat  is  a  ratio  of 
two  like  values.  As  in  the  case  of  specific  gravity,  it  is 
represented  by  an  abstract  number. 

The  Calorim'eter  is  an  instrument  for  measuring  quan- 
tities of  heat.  It  is  made  in  different  forms,  according  to 
the  uses  for  which  it  is  intended. 

Fig.  135  represents  a  calorimeter  used  for  determining  specific  heat. 

The  mass  whose  spe- 
cific heat  is  to  be  as- 
certained, and  whose 
weight  and  tempera- 
ture are  known,  is 
placed  in  a  copper  re- 
ceptacle, surrounded 
by  a  layer  of  ice,  which 
the  cooling  mass  part- 
ly fuses.  The  result- 
ing water  is  drawn 
off  through  a  pipe 
and  weighed.  Each 
gramme  or  pound  of 
water  represents  a  cer- 
tain  number  of  heat 


F,o.  I35.- 


,^M,M^M 

V,zw  or  THE 


ing  body  and  impart- 
ed to  the  ice.     It  requires  about  80  heat  units  to  fuse  1  pound  of  ice 


EQUABLE   CLIMATE. 

(see  page  248).     The  two  inner  compartments  in  the  calorimeter  are 
shielded  from  external  heat  by  an  outer  layer  of  broken  ice. 

The  specific  heat  of  a  number  of  substances  is  herewith  presented : 

Water I'OOOO       Silver      ....       O'OSTO 

Ice 0-489         Tin  .        .        .        .        .        0'0555 

Iron  .       .        . ,'   .        .       0-1138       Lead       .  +   .-.:.;,     .  .  ;.   0'0314 
Copper      .        .      _.        .       0-0939       Mercury.       .       .        .       0'0313 

The  fact  that  water  has  a  high  specific  heat  measurably 
determines  the  equable  character  of  an  oceanic  climate. 
The  water  of  the  ocean  may  part  with  a  large  amount  of 
heat  in  winter  without  getting  cold,  and  may  in  summer 
receive  a  large  amount  without  becoming  warm,  differing 
thus  in  a  marked  degree  from  dry  soil.  The  effect  of  the 
sun  in  producing  a  high  temperature  is  five  times  as  great 
on  dry  sand  as  on  water. 

QUESTIONS.— State  the  general  law  of  expansion.  What  exception  is  there  to  the 
law  that  liquids  are  expanded  by  heat  and  contracted  by  cold  ?  Mention  the 
temperature  at  which  water  is  most  dense.  How  is  this  determined  ?  Explain 
what  occurs  when  a  pond  freezes  over.  Show  what  part  this  provision  of 
Nature  plays  in  the  preservation  of  fish-life.  What  examples  can  you  cite  to 
prove  the  great  force  with  which  water  expands  when  freezing  ?  Can  you 
mention  some  familiar  illustrations  from  your  own  experience  ?  Name  three 
temperatures  that  are  important  for  you  to  remember  in  connection  with  water, 
and  explain  the  significance  of  each.  Illustrate  the  expansion  of  air  by  heat. 
What  is  the  coefficient  of  expansion  of  a  gas  ?  How  do  the  coefficients  of  ex- 
pansion of  gases  differ  ? 

Define  a  heat  unit.  On  what  does  its  magnitude  depend  ?  How  do  we  estimate 
the  temperature  of  a  mixture  of  two  quantities  of  water  differing  in  tempera- 
ture and  weight  ?  Of  two  quantities  of  lead  and  water  ?  Of  equal  quantities 
of  hot  and  cold  water  ?  Explain  Specific  Heat.  Describe  the  calorimeter.  In 
determining  the  specific  heat  of  different  substances,  what  is  assumed  as  a 
standard  ?  Compare  the  standard  with  the  specific  heat  of  other  bodies.  Ex- 
plain the  relative  influence  of  land-masses  and  water  in  modifying  climate. 


FUSION  AND   VAPORIZATION. 

Fusion  illustrated. — Place  a  metallic  vessel  containing 
a  pound  of  water  over  a  Bunsen  flame.  If  a  thermometer 
inserted  in  the  water  shows  a  rise  in  temperature  of  2°  C.  a 
minute,  then  the  flame  is  imparting  to  the  water  two  heat 
units  a  minute. 

If  the  water  be  cooled  down  to  0°  C.  and  a  pound  of  ice 


248  HEAT. 

be  placed  in  the  vessel,  the  flame  remaining  as  before,  the 
temperature  will  continue  at  0°  C.  until  all  the  ice  is  fused. 
If  a  flame  capable  of  imparting  two  heat  units  a  minute  to 
water  at  0°  C.  be  used,  in  a  room  where  the  temperature  is 
0°  C.,  it  will  take  forty  minutes  to  melt  the  ice,  showing 
that  it  requires  eighty  heat  units  to  fuse  one  pound  of  ice. 

To  fuse  a  pound  of  ice  requires  as  much  heat  as  would  raise  the 
temperature  of  80  pounds  of  water  1°,  or  2  pounds  40°.  If  one  pound 
of  ice  at  0°  be  placed  in  10  pounds  of  water  at  8°,  the  water  will  cool 
to  0°,  and  in  so  doing  will  yield  heat  just  sufficient  to  fuse  the  ice. 

PROBLEM.— Five  grammes  of  ice  at  0°  C.  are  placed  in  100  grammes  of  water 
at  90°  C.  Find  the  resulting  temperature. 

The  heat  required  to  fuse  the  ice  is  5  x  80.  The  resulting  ice-cold  water  is 
heated  from  0°  to  <°,  requiring  5  t  heat  units.  The  total  heat  applied  is  therefore 
5  x  80  +  5 1 .  This  heat  is  obtained  from  the  hot  water,  which  cools  down  from  90° 
to  t,  yielding  100  (90  —  t)  heat  units.  Hence  5  x  80  +  5  t  =  100  (90  —  t ),  or  105  t  =  8600, 
or  f  =  81'9. 

When  a  solid  is  converted  into  a  liquid,  heat  is  absorbed.  This  is 
the  principle  on  which  freezing  mixtures  operate.  Ice-cream,  for  in- 
stance, is  frozen  with  a  mixture  of  salt  and  snow  or  pounded  ice ;  the 
latter  is  rapidly  melted,  and  so  much  heat  is  absorbed  in  the  process 
that  the  cream  is  brought  to  a  solid  form. 

Differences  in  Fusibility. — Bodies  differ  widely  in 
fusibility.  Alcohol  has  never  been  rendered  solid,  its  fus- 
ing-point  being  below  the  lowest  attainable  temperature. 
Mercury  fuses  at  —  38-8  C. ;  ice,  at  0°  C. ;  lead,  at  335° ; 
and  iron  at  about  1,500°. 

Substances  like  paper,  wood,  and  cloth,  do  not  fuse  at  high  tem- 
peratures, but  are  decomposed ;  while  carbon  has  neither  been  fused 
nor  decomposed.  Bodies  like  carbon  are  said  to  be  refractory.  The 
number  of  refractory  bodies  has  steadily  diminished  as  methods  of 
producing  higher  temperatures  have  been  invented.  Even  carbon  has 
been  softened. 

Alloys. — When  fused  metals  are  mixed,  they  frequently 
form  a  homogeneous  metal,  known  as  an  Alloy,  having 
different  properties  from  any  of  its  constituents.  Alloys 
usually  fuse  at  lower  temperatures  than  any  of  the  metals 
composing  them. 


LAWS  OF  FUSION.  249 

Rose's  fusible  metal,  consisting  of  4  parts  of  bismuth,  1  of  lead, 
and  1  of  tin,  melts  at  94°  C.,  while  its  most  fusible  component,  tin, 
melts  at  228°  C. 

TABLE   OF    FUSING-POINTS  IN   CENTIGRADE  DEGREES. 

Mercury —  38'8  Bismuth.        .  .      ....  ..  .  264 

Bromine — 12'5  Cadmium         .  .        .•    .  .  .  321 

Ice.        .       .        .        .        .        .  O'O  Lead         .        .  .      •.  •     '.'•   '  -.  335 

Butter +33  Zinc.       .     ._«  ,.       .'     .  .  422 

Rose's  metal       ....  94  Silver       .        .  .        .'       .  .  1,000 

Sulphur        .        .        f      .        .  114  Gold         .        .  .        .        .  '    .  1,250 

Tin.        .       .       .       .       .        .  228  Iron .  1,500 

The  following  Laws  of  Fusion  have  been  deter- 
mined : 

1.  Every  fusible  substance  under  constant  pressure  fuses 
at  a  fixed  temperature,  called  the  f  using-point. 

2.  If  the  pressure  varies,  the  fusing-point  varies  slightly. 

3.  The  fusing-points  of  different  bodies  are  different. 

4.  During   fusion,  the   temperature   remains   constant. 
Increasing  the  temperature  of  the  source  of  heat  causes 
the  body  to  fuse  more  rapidly,  but  does  not  raise  its  tem- 
perature. 

5.  To  fuse  a  gramme  of  any  substance  under  constant 
pressure  requires  a  definite  quantity  of  heat,  which  is  differ- 
ent in  the  case  of  each  fusible  substance. 

Vaporization. — If  a  vessel  containing  1  pound  of  water 
be  heated  by  a  lamp  capable  of  raising  its  temperature  from 
90°  to  100°  C.  in  five  minutes,  then  two  heat  units  will  be 
added  to  the  water  each  minute.  When  100°  is  reached, 
the 'temperature  will  cease  to  rise,  although  two  heat  units 
a  minute  are  still  being  added  to  the  water.  The  heat  is 
now  being  used  in  the  vaporization  of  the  liquid.  It  will 
require  268'5  minutes  to  evaporate  (convert  into  a  gaseous 
state)  the  pound  of  water  with  such  a  flame.  Hence  the 
heat  required  to  evaporate  the  water  is  537  units. 

When  a  gramme  of  steam  condenses  to  water  without  any  change 
of  temperature,  the  heat  required  to  raise  the  temperature  of  537 
grammes  of  water  1°  C.  is  evolved.     Such  is  the  source  of  heat  in  the 
steam  coils  used  in  warming  buildings. 
17 


250  HEAT. 

Phenomena  of  Evaporation. — Some  substances,  like 
musk,  camphor,  and  ammonium  carbonate,  vaporize  without 
going  through  a  process  of  fusion.  Moreover,  a  high  tem- 
perature is  not  essential  to  vaporization.  At  ordinary  tem- 
peratures, wherever  a  surface  of  water  is  in  contact  with  the 
air,  vapor  is  formed,  and  by  this  means  the  atmosphere  be- 
comes charged  with  moisture.  Whenever  vapor  is  formed, 
heat  is  absorbed,  and  cold  is  produced. 

Hence,  when  the  skin  is  moistened  with  a  volatile  liquid  like  ether 
or  cologne  water,  a  sensation  of  cold  is  experienced.  Fanning-cools 
the  face  by  rapidly  vaporizing  the  insensible  perspiration  which  Na- 
ture has  provided  to  regulate  the  temperature  of  the  body.  The 
cooling  which  accompanies  the  evaporation  of  sweat  is  one  means  of 
preventing  the  bodily  temperature  from  rising  above  the  natural 
standard  of  98'5°.  A  high  external  temperature  can,  therefore,  be 
borne  as  long  as  the  skin  responds  with  an  increased  secretion  of 
perspiration.  Sculptors  have  worked  with  safety  in  dry  ovens  at  a 
temperature  of  more  than  100°  Fahr.  above  the  boiling-point  of  water. 

A  drop  of  water  let  fall  on  a  cold  iron  moistens  its  surface ;  if  let 
fall  on  a  very  hot  iron,  it  hisses  and  runs  off  without  leaving  any  trace 
of  moisture.  In  the  latter  case,  the  water  does  not  touch  the  iron  at 
all,  but  is  separated  from  it  by  a  layer  of  steam.  Laundresses  try 
their  irons  with  wet  fingers,  to  see  if  they  are  hot  enough  for  use. 
On  the  same  principle,  jugglers  plunge  their  hands  into  melted  metal 
with  impunity,  by  first  wetting  them.  The  drops  of  moisture  on  their 
hands  assume  a  spheroidal  form,  and  in  this  state  evaporate  much 
more  slowly  than  at  a  lower  temperature,  keeping  the  molten  metal 
from  contact  with  the  skin.  This  condition,  which  is  assumed  by 
liquids  when  exposed  to  the  action  of  very  hot  metals,  is  known  as  the 
SPHEROIDAL  STATE. 

Phenomena  of  Boiling1. — When  a  glass  flask  partly 
filled  with  water  is  heated,  bubbles  of  air  become  visible  on 
its  sides.  They  appear  at  a  low  temperature,  and  may  even 
be  seen  in  a  vessel  of  water  standing  in  sunlight. 

Finally,  as  the  temperature  nears  the  boiling-point,  bub- 
bles of  steam  begin  to  form  at  the  bottom  of  the  flask,  rise, 
and  collapse  with  a  sharp,  snapping  sound.  The  upper  por- 
tions of  the  liquid  being  somewhat  cooler  than  those  below, 


BOILING-POINTS. 


251 


the  steam  on  rising  condenses,  and  the  walls  of  the  bubbles, 

under  the  pressure  of  the  atmosphere,  come  together  with  a 

crash.     This  sound  of  the  collapsing 

bubbles  is  heard  in  the  singing  of  the 

tea-kettle,  and  can  be  rendered  more 

audible  if  steam  from  a  boiler  or  coil 

is  passed  through  a  rubber  tube  into 

cold  water.     In  a  few  moments  the 

bubbles  cease  to  collapse,  but  grow 

larger  as   they  rise,  and   the  liquid 

then  begins  to  boil  freely. 


Boiling-Points  differ. — As  the 

fusing-points  of  substances  vary,  so 
do  the  temperatures  at  which  they 
boil.  Liquids  which  boil  at  low  tem- 
peratures are  said  to  be  volatile. 

If  a  test  -  tube  containing  ether  be 
dipped  into  a  beaker  of  water  having  a 
temperature  of  50°  or  60°  C.,  the  ether 
will  begin  to  boil,  and  a  thermometer  placed 
in  the  ether  will  indicate  a  temperature  of 

35°  C.  If  the  water  is  warmer,  the  ether  will  boil  more  briskly,  but  its 
temperature  will  remain  unchanged.  The  heat  required  to  vaporize 
the  ether  will  be  taken  from  the  water,  which  will  therefore  cool  more 
quickly  than  it  would  if  the  ether  were  not  evaporating. 

Remember,  it  is  dangerous  to  bring  a  flame  near  boiling  ether. 


FIG.  136.— PHENOMENA  OP 
BOILINO. 


TABLE   OF   BOILING-POINTS   IN   CENTIGRADE   DEGREES. 


Ammonia  .  -  ^ 
Sulphur  dioxide  . 
Ether  .  .  . 
Carbon  bisulphide 
Alcohol  . 


—  40  Water     . 

—  8  Mercury 

35  Sulphur . 

48  Cadmium 

78  Zinc 


100 
350 
447 
860 
1040 


Laws  of  Boiling. — From   the   experiments  described 
above  you  have  learned  two  important  laws  of  boiling : 

1.  Every  substance  has  a  definite  temperature  at  which 
it  boils. 

2.  This  temperature  remains  constant  during  boiling. 


252 


HEAT. 


Distillation. — If  any  liquid  is  required  to  be  separated 
from  a  salt  which  it  holds  in  solution  in  such  a  manner  as 
to  save  the  liquid,  the  solution  must  be  heated  in  a  retort  or 
boiler  known  as  a  "  still,"  shown  in  Fig.  137.  The  vapor 
passes  into  a  tube  or  worm  (d  d),  surrounded  by  cool  water 
or  ice,  and  is  thus  condensed  and  collected  in  a  vessel  called 
a  "  receiver  "  (g).  The  salt  remains  behind  in  the  retort. 
This  process  is  called  Distillation,  and  it  is  possible  because 
some  substances  are  converted  into  vapor  at  lower  tempera- 
tures than  others. 


FIG.  137.— A  STILL. 

Alcohol  and  other  volatile  liquids  can  be  separated  from 
water  by  the  same  apparatus.  The  temperature  of  the  re- 
tort is  raised  to  or  slightly  above  the  boiling-point  of  the 
more  volatile  liquid,  which  then  passes  off  as  vapor,  leaving 
the  less  volatile  liquid  behind  in  the  retort.  A  little  of  the 
latter  is  indeed  carried  over,  particularly  toward  the  last,  so 
that  the  first  part  of  the  distillate  is  sometimes  collected  in 
a  separate  vessel.  Further  purification  can  be  effected  by 
repeated  distillation. 


DISTILLATION. 


253 


FIG.  138.— SIMPLE  DISTILLATION. 


The  pupil  may  readily  improvise  a  simple  still  with  a  glass  retort, 
retort-receiver,  and  common  tin  basin  filled  with  cold  water.  If  pro- 
vided with  a  condenser  (Fig.  10,  page  230)  he  should  arrange  it,  by 
the  aid  of  corks  and  glass  or  rubber  tubing,  between  the  receiver  and 
the  retort.  If 
water  be  placed 
in  the  retort  and 
a  flame  applied 
till  it  boils,  the 
steam  formed 
will  condense 
and  trickle  down 
into  the  receiv- 
er as  chemical- 
ly pure  distilled 
water.  Mere 
boiling  will  free 
water  from  gas- 
eous impurities 
and  also  destroy 
the  active  prin- 
ciples of  disease.  It  is  safe,  therefore,  to  drink  boiled  or  distilled 
water  during  the  prevalence  of  epidemics. 

Distill  a  small  quantity  of  salt  or  sea  water.  The  water  in  the  re- 
ceiver will  have  a  disagreeable,  flat  taste,  because  it  is  not  aerated,  or 
does  not  contain  air,  as  all  drinkable  water  should.  Shake  it  repeat- 
edly in  a  large  clean  bottle  and  it  will  lose  its  unpleasant  taste. 

Introduce  some  fragrant  roses  into  the  retort  with  water  and  ap- 
ply heat.  The  essential  oil  of  the  flowers,  known  as  attar,  will  pass 
over  with  the  steam,  imparting  a  perceptible  perfume  to  the  water 
that  condenses  in  the  receiver.  Large  quantities  of  flowers  are  dis- 
tilled in  this  way;  the  oils  float  and  are  removed.  Dissolved  in 
cologne  spirit,  they  constitute  perfumery  extracts. 

QUESTIONS.— What  do  you  understand  by  fusion  ?  Illustrate  your  answer.  How 
much  heat  is  required  to  fuse  a  pound  of  ice  ?  How  many  thermal  units  ?  On 
what  principle  do  freezing  mixtures  operate  ?  Do  all  bodies  fuse  at  the  same 
temperature  ?  Illustrate  the  difference,  as  regards  their  capability  of  being 
melted,  in  wax,  mercury,  alcohol,  lead,  gold.  What  is  meant  by  a  refractory 
body,  and  what  is  probable  of  all  refractory  bodies  ?  Define  an  alloy.  Formu- 
late a  general  rule  for  the  fusing-points  of  alloys.  Sum  up  the  laws  of  fusion. 

What  is  vaporization  ?  Mention  the  successive  effects  of  heat  on  solids.  May  » 
body  vaporize  without  fusing  ?  Is  heat  essential  to  vaporization  ?  Prove  that 
cold  is  produced  when  vapor  is  formed.  Why  is  this  ?  Why  does  fanning  cool 


254  HEAT. 

the  face  ?  Can  you  explain  the  office  of  perspiration.  Describe  the  spheroidal 
state,  and  explain  what  practical  advantage  may  be  taken  of  the  tendency  of 
liquids  to  assume  this  condition.  What  is  the  temperature  of  water  in  the 
spheroidal  state  ?  Only  about  95°  C. 

Describe  the  phenomena  of  boiling.  Explain  the  singing  of  the  tea-kettle.  Does 
the  temperature  of  a  liquid  alter  during  boiling  ?  Do  all  liquids  vaporize  at  the 
same  temperature  ?  Contrast  ether  with  water  in  this  respect.  \V  hat  is  dis- 
tillation, and  on  what  fact  is  the  process  based  ?  What  is  an  apparatus  for 
distilling  called  ?  Describe  the  still.  Explain  how  a  simple  still  may  be  im- 
provised. How  may  pure  water  be  obtained  by  the  use  of  this  still  ?  How,  the 
essential  oils  of  flowers  ?  Why  is  not  distilled  water  palatable  ? 


INFLUENCE  OF  PRESSURE  ON  FUSING  AND 
BOILING  POINTS. 

Boiling-  and  Fusing  Points  vary  according  to  the 
pressure.  When  a  substance  expands  in  solidifying,  as  in 
the  case  of  water  and  some  of  the  metals,  the  operation  is 
resisted  by  atmospheric  pressure.  If  water  at  0°  could  be 
prevented  from  expanding  by  inclosing  it  in  a  vessel  of 
sufficient  strength,  it  would  not  freeze  if  cooled  far  below 
the  freezing-point.  If  ice  at  0°  is  put  under  a  pressure  of 
20  atmospheres,  it  will  fuse.  In  fusing,  it  diminishes  in  vol- 
ume, and  the  increased  pressure  aids  the  operation.  Water 
under  such  pressure  would  not  freeze  until  it  had  cooled 
0-15°  below  0°  C. 

If  the  pressure  on  the  ice  be  less  than  one  atmosphere,  it 
will  not  fuse  at  0°  but  at  a  slightly  higher  temperature,  be- 
cause the  aid  which  the  operation  derives  from  atmospheric 
pressure  is  diminished. 

In  the  case  of  substances  which  contract  in  solidifying,  all  these 
statements  would  be  reversed.  Iron  and  type-metal  expand  when 
they  solidify,  and  therefore  fill  molds  and  make  sharp  castings.  The 
reverse  is  true  of  silver  and  gold.  Coins  made  of  these  metals  are 
therefore  stamped  with  a  die. 

Water  expands  greatly  on  vaporizing.  A  cubic  inch  of 
water  will  make  about  a  cubic  foot  of  steam  at  one  atmos- 
phere pressure.  The  formation  of  steam  is  resisted  by  press- 
ure ;  hence  if  the  pressure  be  more  than  one  atmosphere,  the 
water  must  be  made  hotter  than  100°  before  it  will  boil. 


BOILING-  BELOW  100a  C, 


255' 


Conversely,  if  the  pressure  on  the  water  is  diminished,  the  water 
will  boil  at  a  lower  temperature  than  100°  C.  On  Pike's  Peak,  at  an 
altitude  of  14,000  feet,  where  the  barometer  column  may  be  only  18 
inches  high,  the  temperature  of  boiling  water  is  only  188°  Fahr.,  or 
86-6°  C.  At  such  places  food  which  is  cooked  by  boiling  water  requires 
a  much  longer  time  for  its  preparation  than  at  the  sea-level. 

Diminishing  the  pressure, 
therefore,  raises  the  freezing- 
point  of  water  slightly  and 
lowers  the  boiling-point  very 
much  more.  On  this  princi- 
ple, vacuum-pans  are  now  used 
for  the  evaporation  of  sugar 
solutions.  Under  the  receiver 
of  an  air-pump,  the  boiling- 
point  may  even  be  brought 
down  to  the  freezing-point, 
so  that  boiling  and  freezing 
may  be  going  on  at  the  same 
time. 

Boiling  at  Temper- 
atures below  1OO°  C — 

The  boiling  of  water  at  a 

reduced  temperature  and 

pressure  is  illustrated  in 

Fig.    139.       A   Florence 

flask  half  filled  with  water 

is  closed   tightly  with   a 

cork,      through      which 

pass  a  thermometer  and 

a  glass  tube.     The  latter  terminates  just  beneath  the  cork, 

and  its  other  extremity  is  bent  downward  into  a  vessel  of 

cold  water  standing  at  some  distance  below  the  flask. 

The  water  in  the  flask  is  heated  to  boiling,  and  its  temperature  is 
noted  by  the  thermometer  when  it  discharges  into  the  open  air,  and 
also  when  the  lower  end  of  the  tube  is  immersed  in  the  iced  water.  In 
the  latter  case,  the  water  in  the  flask  will  be  seen  to  boil  at  a  temper- 
ature below  100°,  and  the  iced  water  may  rise  in  the  tube.  This  rise 
of  the  water  may  be  increased  by  clamping  ice-blocks  around  the  tube 


FIG.  139.— BOILING  BELOW  100°  C.,  212°  F. 


256 


HEAT. 


and  moving  them  up  and  down  so  as  to  cool  the  whole  tube,  or  by  sur- 
rounding the  tube  with  ice  in  a  vessel,  as  in  the  figure.  The  pressure 
within  the  flask  is  less  than  the  atmospheric  pressure  by  the  pressure 
due  to  the  column  of  water  in  the  tube. 

If  the  flame  be  removed,  the  lower  end  of  the  tube  closed 
by  the  finger,  and  the  flask  then  wrapped  with  a  cold  wet 
cloth,  the  water  in  the  flask  will  begin  to  boil  vigorously. 
This  is  due  to  the  condensation  of  the  steam  in  the  upper 
part  of  the  flask,  which  reduces  the  internal  pressure  and 

thus  causes  the 
water  to  boil 
below  100°  0. 
If  the  flask  is 
dipped  in  cold 
water,  the  ex- 
periment will 
be  still  more 

FIG.  140.— EXPERIMENT  WITH  THE  PULSE-GLASS.  Striking. 

The  same  phenomenon  may  be  shown  with  a  pulse-glass  contain- 
ing colored  ether  (Fig.  140).  One  bulb  is  surrounded  with  ice  or  snow, 
and  the  other  is  then  placed  in  hot  water.  The  hot  water  causes  the 
ether  to  boil,  and  the  vapors  are  condensed  in  the  second  bulb. 

Boiling  under  High  Pressure. — In  an  ordinary  steam- 
boiler,  if  the  steam  is  not  drawn  off  or  condensed,  evapora- 
tion apparently  soon  ceases.  The  steam  space  is  then  said 
to  be  saturated.  Particles  of  water  are  indeed  still  flying 
off  from  the  surface  of  the  water  into  the  steam  space 
above,  but  this  space  is  so  full  of  particles  that  an  equal 
number  are  continually  plunging  down  upon  the  water  sur- 
face and  becoming  part  of  the  liquid.  If  the  fire  is  now 
made  hotter,  the  molecular  agitation  of  the  water  is  in- 
creased, so  that  particles  are  shaken  loose  from  the  water 
surface  in  greater  numbers  than  they  are  returned  ;  but  this 
crowds  the  steam  space  more  densely,  and  very  soon  equi- 
librium is  again  reached.  The  steam  space  is  saturated  at 
a  higher  temperature  and  pressure. 


BOILING  UNDER  HIGH  PRESSURE. 


257 


If  steam  is  drawn  off  to  feed  an  engine  or  to  heat  rooms,  then 
evaporation  will  go  on  continuously,  the  boiling-point  depending  upon 
the  resulting  boiler  pressure.  With  increasing  pressure,  there  is  no 
limit  to  the  rise  in  the  boiling-point  except  the  strength  of  the  boiler. 
The  temperature  of  boiling  water  under  pressures  ranging  from  one 
to  ten  atmospheres  is  given  in  the  following  table  : 


Pressure  in 
atmospheres. 

Centigrade 
temperature. 

Fahrenheit 
temperature. 

Pressure  in 
atmospheres. 

Centigrade 
temperature. 

Fahrenheit 
temperature. 

1 
2 
3 
4 
5 

100-0 

1206 

133-9 
144-0 
152-2 

212-0 
249-1 
273-1 
291-2 
306-0 

6 
7 
8 
9 
10 

156-2 
165-3 
170-8 
175-8 
180-3 

313-2 
329-5 
339-4 
348-4 
356-5 

In  a  locomotive-boiler,  the  pressure  is  about  ten  atmos- 
pheres, and  the  temperature  of  the  water  and  steam  in  the 
boiler  is  then  180°  C. 

The  following  table,  which  forms  the  basis  for  observations  on 
atmospheric  humidity,  gives  the  vapor  pressure  in  inches  of  mer- 
cury in  a  boiler  corresponding  to  various  temperatures,  from  0°  Fahr. 
to  101°  Fahr.  Thus,  at  32°  Fahr.,  where  the  boiler  is  surrounded  by 
ice-water,  the  vapor  pressure  within  would  be  0-181  inch  of  mercury. 

STEAM   PRESSURE  IN  INCHES   OF   MERCURY   AT   TEMPERATURES   t. 


t 

Pressure. 

t 

Pressure. 

t 

Pressure. 

t 

Pressure. 

0 

0-043 

33 

0-188 

56 

0-449 

79 

0-990 

2 

0-048 

34 

0-196 

57 

0-465 

80 

1-088 

4 

0-052 

35 

0-204 

58 

0-482 

81 

1-057 

6 

0-057 

36 

0-212 

59 

0-500 

1'092 

8 

0-062 

37 

0-220 

60 

0-518 

83 

1-128 

10 

0-068 

38 

0-229 

61 

0-536 

84 

1'165 

12 

0-075 

39 

0-238 

62 

0-556 

85 

1'203 

14 

0-082 

40 

0-248 

63 

0-576 

86 

1-242 

16 

0-090 

41 

0-257 

64 

0-596 

87 

T282 

18 

0-098 

42 

0-267 

65 

0-617 

88 

1-323 

20 

0-108 

43 

0-277 

66 

0639 

89 

T366 

21 

0-113 

44 

0-288 

67 

0-662 

90 

1'410 

22 

0-118 

45 

0-299 

68 

0-685 

91 

1  '455 

23 

0-123 

46 

0-311 

69 

0-708 

92 

1'501 

24 

0-129 

47 

0-323 

70 

0-733 

93 

1-548 

25 

0-135 

48 

0-335 

71 

0-758 

94 

1-597 

26 

0-141 

49 

0-348 

72 

0-784 

95 

•647 

27 

0-147 

50 

0-361 

73 

0-811 

96 

•698 

28 

0-153 

51 

0-374 

74 

0-839 

97 

'751 

29 

0-160 

52 

0-388 

75 

0-868 

98 

'805 

30 

0-167 

53 

0-403 

76 

0-897 

99 

1-861 

31 

0-174 

54 

0-418 

77 

0-927 

100 

1'918 

32 

0-181 

55 

0-433 

78 

0-958 

101 

1-977 

258 


HEAT. 


The  apparatus  by  means  of  which  the  values  of  the  last  table  were 
obtained  is  shown  in  Fig.  141.  A  copper  vessel,  C,  serves  as  the  boiler. 
This  is  partly  filled  with  water,  into  which  four  thermometers  dip  to 
various  depths.  The  thermometers  fit  into  air-tight 
packing  in  the  cover,  and  the  mercury  can  be  read 
above.  By  means  of  a  tube,  A  B,  the  steam  space  in 
the  boiler  connects  with  a  glass  globe  contained  in 


FIG.  141. — APPARATUS  FOR  M 


5SURE    CORRESPONDING  TO 


DIFFERENT  TEMPERATURES. 


the  vessel,  M,  having  a  capacity  of  about  six  gallons  and  filled  with  air. 
To  the  upper  part  of  the  globe  is  attached  a  tube  with  two  branches. 
One  of  these  connects  with  an  instrument  which  measures  the  pressure 
within  the  globe,  tube,  and  boiler.  The  other  communicates  at  H 
with  a  compressing  or  exhausting  air-pump,  by  means  of  which  the 
pressure  can  be  varied  at  will.  The  globe  in  M  is  kept  cool  by  sur- 
rounding it  with  water,  and  cool  water  is  passed  through  the  jacket 
which  encompasses  the  tube  A  B. 

When  the  water  in  C  is  boiled,  the  steam  condenses  in  the  pipe 
and  globe  and  runs  back  into  the  boiler.  Whenever  the  pressure 
is  fixed,  whether  produced  by  the  generation  of  steam  or  by  the  forcing 
of  air  into  the  globe,  the  temperature  is  always  the  same.  For  in- 


PRESSURE  OF  VAPOR  BELOW  0°  C.  259 

stance,  whenever  the  pressure  inside  is  reduced  to  Q'22  inch  of  mer- 
cury, the  water  boils  at  37°  Fahr.  and  can  not  be  heated  above  that 
temperature  if  the  pressure  is  held  constant.  Making  the  flame  under 
the  boiler  hotter  will  cause  the  water  to  evaporate  more  rapidly,  but 
will  not  raise  its  temperature. 

Pressure  of  Vapor  below  the  Freezing-Point. — If 

the  connection  with  the  air-pump  be  opened  so  that  the 
steam  will  drive  all  the  air  from  the  apparatus,  and  if  the 
pipes  be  then  closed  and  the  vessel  and  boiler  be  put  into 
ice-water,  the  steam  will  nearly  all  condense.  There  will, 
however,  still  be  a  pressure  of  0-181  inches  of  mercury  in 
the  boiler.  If  the  boiler  be  cooled  to  —  30°  Fahr.,  the  press- 
ure will  diminish  to  0-009  inch  of  mercury. 

Even  at  such  low  temperatures,  ice  slowly  evaporates. 
In  this  way  wet  clothes  become  dry  in  freezing  weather,  and 
snow  and  ice  slowly  disappear,  although  the  temperature 
may  be  continuously  below  the  freezing-point.  Probably  if 
ice  were  cooled  to  — 75°  C.  it  would  not  appreciably  evapor- 
ate, but  would  behave  as  lead  or  zinc  at  ordinary  tempera- 
tures. At  higher  temperatures,  these  substances  themselves 
may  be  vaporized. 


QUESTIONS.— State  fully  the  influence  of  pressure  on  fusing  and  boiling  points. 
How  may  water  be  prevented  from  freezing  at  a  temperature  below  0*  C.  ? 
Why  can  iron  be  molded  better  than  either  silver  or  gold  ?  To  how  great  a  de- 
gree does  water  expand  on  vaporizing  ?  Under  what  circumstances  will  water 
not  boil  at  100°  C.  ?  When  will  it  boil  at  a  lower  temperature  ?  Will  it  then 
cook  food  ?  The  Dead  Sea  is  1,272  feet  below  sea-level.  At  what  temperature 
does  water  boil  on  its  shore  ?  At  about  214*  Fahr. 

Illustrate  the  boiling  of  water  at  a  reduced  temperature  and  pressure.  The  boil- 
ing of  ether.  In  Fig.  140,  page  256,  if  the  cold  bulb  is  removed  from  the  ice 
while  the  other  remains  in  the  hot  water,  the  apparatus  will  quickly  explode. 
Why  ?  Describe  the  phenomena  of  boiling  under  high  pressure  in  an  ordinary 
steam-boiler.  How  will  the  temperature  vary  ?  Under  a  pressure  of  ten  at- 
mospheres, what  is  the  boiling-point  of  water  ?  Name  the  only  limit  to  the 
rise  in  the  boiling-point.  State  the  pressure  in  locomotive-boilers. 

Explain  the  apparatus  by  which  the  steam  pressures  corresponding  to  different 
temperatures  are  ascertained.  Why  is  the  temperature  always  the  same  when 
the  pressure  is  constant  ?  What  effect  is  apparent  on  increasing  the  heat  ap- 
plied to  the  boiler  ?  What  can  you  say  of  the  vapor  pressure  below  the  freez- 
ing-point ?  Does  ice  evaporate  at  low  temperatures  ?  Is  there  any  conceivable 
temperature  at  which  snow  and  ice  would  not  slowly  disappear  ? 


260 


HEAT. 


HUMIDITY  OF  THE  ATMOSPHERE.— VAPOR 
PRESSURES. 

The   Atmosphere   always   contains  Water- Vapor, 

but  is  rarely  if  ever  saturated,  so  that  no  further  evapora- 
tion can  take  place  from  bodies  in  contact  with  it.  Steam 
from  a  tea-kettle  is  invisible  for  about  an  inch  from  the 
spout.  It  eventually  condenses  into  a  cloud  of  minute 
water-globules,  which  evaporate  quickly  In  a  saturated 
atmosphere,  the  cloud  would  not  evaporate. 

Atmospheric  Humidity. — The  weight  of  moisture  in  a 
unit  volume  of  the  air  (in  grains  to  the  cubic  foot,  or  in  milli- 
grammes to  the  cubic  metre)  is  called  its  Humidity.  It  may 
be  measured  by  means  of  the  apparatus  shown  in  Fig.  142. 


FIG.  142.— MEASUREMENT  OP 
ATMOSPHERIC  HUMIDITY. 

An  aspirator  bottle  (C)  nearly  filled  with 
water  is  provided  with  a  siphon,  through  which 

the  liquid  may  be  drawn  off.  The  air  space  in  the  bottle  is  connected, 
as  shown,  with  two  U-tubes  containing  fragments  of  chloride  of  cal- 
cium, or  pumice-stone  impregnated  with  sulphuric  acid.  When  the 
water  runs  out  of  the  bottle,  air  enters  to  supply  its  place  through  the 
U-tubes.  The  first  tube,  A,  absorbs  all  the  moisture  from  the  air, 
while  the  second  tube,  B,  intercepts  any  moisture  which  may  proceed 
from  the  bottle. 


DEW-POINT. 


261 


Measure  the  volume  of  the  water  that  has  run  out.  This  is  equal 
to  the  volume  of  air  which  has  passed  through  the  apparatus.  Tubes  A 
and  B  are  weighed  before  and  after  the  experiment.  The  increase  in 
weight  gives  the  moisture  in  the  measured  volume  of  air,  from  which 
the  moisture  in  grains  to  the  cubic  foot  can  be  found.  The  humidity 
in  grains  to  the  cubic  foot  for  saturated  air  is  given  in  the  accom- 
panying table  for  various  temperatures: 


Degrees  F. 

Humidity. 

Degrees  F. 

Humidity. 

Degrees  F. 

Humidity. 

0 

0'44 

30 

1-27 

60 

3-35 

10 

0-64 

40 

1  77 

70 

4'53 

20 

0'90 

50 

2-44 

80 

6-08 

Dew-Point. — If  a  tin  cup  containing  water  is  cooled 
gradually  by  adding  small  pieces  of  ice  and  stirring  the 
water,  moisture  will  finally  condense  on  the  outside  of  the 
cup  in  the  form  of -dew.  Drops  of  water  are  frequently 

observed  on  water-pitchers  in  summer.     If  the  cup  contains 

T 


FIG.  143.— REGNAULT'S  HYGROMETER. 

a  small  fragment  of  ice,  when  the  dew  is  first  observable,  re- 
move the  ice  at  once  and  observe  the  temperature  of  the 
water.  Allow  the  water  to  stand  until  the  dew  disappears, 
and  again  observe  the  temperature,  keeping  the  water 
stirred.  The  mean  of  these  two  temperatures  is  the  dew- 


262 


HEAT. 


point.  If  the  air  were  to  be,  cooled  to  this  temperature,  it 
would  be  saturated  with  moisture,  and  any  further  cooling 
would  precipitate  the  moisture  as  a  cloud. 

The  most  suitable  apparatus  for  determining  the  dew-point  is 
Regnault's  (reh-no1)  hygrometer,  shown  in  Fig.  143.  It  consists  of  two 
glass  tubes,  one  of  which  (D)  connects  by  means  of  a  T-tube  with  an 
aspirator  A.  Both  tubes  contain  thermometers  fitted  into  their  stop- 
pers. The  tube  connecting  with  the  aspirator  has  also  an  air-tube  pass- 
ing nearly  to  the  bottom,  and  is  in  part  filled  with  ether.  When  water 
puns  from  the  aspirator,  air  is  drawn  through  the  ether,  which  vapor- 
izes, cooling  the  remaining  ether  and  the  tube. 
When  dew  is  observable  on  the  silver  thimble 
which  caps  the  lower  end  of  the  tube,  the 
water  is  checked  and  the  thermometers  are 
both  read.  The  ether  is  now  allowed  to  warm  up 
until  the  dew  disappears,  and  the  thermometers 
are  again  read.  The  mean  of  the  two  readings  of 
the  cooled  thermometer  is  the  dew-point.  The 
other  thermometer  registers  at  the  same  time  the 
air  temperature. 

A  simple  apparatus,  which  will  give  very  good 
results,  may  be  made  from  an  ordinary  test-tube 
partly  filled  with  ether,  containing  a  thermometer, 
and  a  glass  tube  connected  with  a  rubber  coil  two 
or  three  feet  in  length  (see  Fig.  144).  Air  is  blown 
through  the  tube,  vaporizing  a  portion  of  the  ether 
and  thus  producing  cold.  Follow  the  same  direc- 
tions as  in  the  case  of  Regnault's  hygrometer,  and 
determine  the  dew-point.  The  air  temperature 
may  be  ascertained  from  an  ordinary  thermometer. 

Relative  Humidity. — Suppose  the  air 
temperature  to  be  70°  F.  and  the  dew-point 
58°  F.  If  the  air  were  cooled  down  to  58°, 
it  would  be  saturated  with  moisture.  From 
the  table  of  pressures  of  vapor  (page  257) 
it  will  be  seen  that  saturated  vapor  at  a 
temperature  of  58°  has  a  pressure  of  0'482  inch  of  mercury. 
This  much  of  the  atmospheric  pressure  shown  by  the  barom- 
eter is  due  to  moisture. 


FIG.  144.— SIMPLE  Ap* 

PARATUS  FOR  DETER. 
MINING  THE  DEW. 

POINT. 


RELATIVE   HUMIDITY.  263 

If  the  air  were  saturated  with  moisture  at  70°,  its  vapor 
pressure  would  be  0-733  inch  of  mercury.  The  amount  of 
moisture  to  the  cubic  foot  would  then  be  greater  than  it  is 
at  58°  in  the  ratio  0-733  -f-  0-482.  The  amount  of  moisture 
actually  in  each  cubic  foot  of  air  would  be  a  certain  fraction 
of  what  that  cubic  foot  would  contain  if  saturated.  That 
fraction  is  0-482  +  0-733  =  0-65. 

The  relative  humidity  is  the  ratio  of  the  amount  of 
moisture  in  the  air  to  the  amount  required  to  produce  sat- 
uration. In  the  case  instanced  above,  the  relative  humid- 
ity is  65  per  cent.  At  70°,  the  air  could  hold  4-53  grains 
per  cubic  foot.  Hence,  at  58°,  it  would  hold  65  per  cent  of 
4-53,  or  2-94  grains. 

When  the  Relative  Humidity  is  low — that  is,  when 
the  air  is  dry — we  feel  little  inconvenience,  even  if  it  is 
very  warm.  Perspiration  rapidly  evaporates,  and  its  latent 
heat  is  thus  taken  from  the  body,  keeping  it  cool.  If  the 
air  were  saturated,  its  relative  humidity  would  be  1-00,  or 
one  hundred  per  cent.  No  evaporation  could  then  take 
place,  and  temperatures  would  prove  fatal  which  could  be 
endured  with  impunity  in  dry  air. 

When  it  is  dry  and  hot,  one  feels  cooler  during  exercise  in  the 
sunshine  and  open  air  than  when  sitting  in  the  house.  Why  ?  In  the 
vapor-laden  atmosphere  of  the  oceanic  tropics  we  find  a  condition 
which  interferes  seriously  with  active  bodily  exercise. 

In  Meteorological  Stations,  relative  humidity  is  usu- 
ally determined  by  the  psychrometer  (si-krom'e-ter),  or  the 
wet  and  dry  bulb  thermometers,  shown  in  Fig.  145.  The 
bulb  of  one  thermometer  is  covered  with  clean  unstarched 
cotton  cloth,  which  dips  into  a  vessel  of  rain  or  distilled 
water.  By  capillary  action  the  cloth  is  always  kept  wet. 
Evaporation  of  the  water  cools  the  bulb,  the  heat  of  evapora- 
tion being  taken  in  part  from  it.  If  the  air  is  dry,  evapora- 
tion goes  on  more  rapidly,  and  the  depression  of  the  mercury 
column  is  greater  than  when  the  air  is  nearly  saturated. 


264 


HEAT. 


If  the  air  is  wholly  saturated,  the  wet  bulb  shows  the 
same  temperature  as  the  dry  one,  both  reading  at  the  dew- 
point.  The  dry  bulb  indicates 
the  air  temperature.  The  wet 
bulb,  however,  always  reads 
higher  than  the  dew-point,  ex- 
cept in  the  case  just  men- 
tioned. 

For  example,  in  a  certain  case, 
the  dry  bulb  read  70°,  the  wet  bulb 
63-2°,  and  the  hygrometer  at  the  same 
time  showed  the  dew-point  to  be  58°. 
The  wet  bulb  there- 
fore read  6-8°  below 
the  dry  bulb,  and  the 
dew-point  was  12°  be- 
low it — see  diagram.  12  ( 

Now,  if  6'8  were 
multiplied  by  some 
factor,  the  product 
would  be  12,  or  the 
difference  between  the  dew-point  and 
the  air  temperature.  The  factor  in 

12 

this  instance  is  evidently  ^  =  1'76. 
b'o 

Unfortunately,  this  factor  is  dif- 
ferent for  different  temperatures,  so 
it  must  be  determined  for  all  ordi- 
nary temperatures.  The  numbers  obtained  are  called  Glaisher's  fac- 
tors. They  are  given  in  the  table  below : 


-70 


-63-2 


L-58 


FIG.  145.— WET  AND  DRY  BULB  THER- 
MOMETER. (LATEST  U.  S.  SIGNAL 
SERVICE  PATTERN.) 


Dry  bulb." 
Temperature  F.° 

Factor. 

Dry  bulb. 

Temperature  F.° 

Factor. 

Dry  bulb. 
Temperature  F.° 

Factor. 

Below  24° 
24-25 
25-26 
26-27 
27-28 
28-29 
29-30 

8'5 

6'9 
6-5 
6-1 
5'6 
5-1 
4-6 

30-31° 
31-32 
32-33 
33-34 
34-35 
35-40 
40-45 
45-50 

41 

3-7 
3-3 
3-0 
2-8 
2'5 
2-2 
2-1 

50-55° 
55-60 
60-65 
65-70 
70-75 
75-80 
80-85 

2-0 
1-9 
1-8 
1-8 
1-7 
1-7 
1-6 

THE  PSYCHROMETER.  265 

If  the  temperature  were  26°  Pahr.,  the  bulb  would  be  covered  with 
ice.  In  freezing  weather  it  is  better  to  remove  the  cloth  and  wet  the 
bulb,  allowing  a  thin  film  of  ice  to  form  upon  it.  If  the  wet  bulb 
reads  24-5°,  then  the  dew-point  would  be  (26—24-5)  x  6-3  =  9-4  degrees 
below  the  air-temperature.  The  dew-point  would  therefore  be  26—9-4 
=  16-6.  The  value  of  the  factor  for  26  is  taken  midway  between  the 
values  6-1  and  6'5  in  the  table.  This  method  is  not  quite  accurate  for 
low  temperatures. 

The  Sling  Psychrometer. — The  psychrometer  is  most 
trustworthy  when  used  in  the  wind.  The  air  immediately 
around  the  wet  bulb  becomes  moist,  and  evaporation  from 
it  will  depend  upon  the  quickness  with  which  this  air  is 
removed  by  wind.  The  humidity  of  the  air  out  of  doors  is 
therefore  determined  by  means  of  a  psychrometer  in  which 
the  wet  bulb  is  moved  through  the  air  until  it  shows  a  con- 
stant reading. 

A  simple  and  inexpensive  whirling  psychrometer — consisting  of 
two  thermometers  with  the  degrees  marked  on  the  glass  tubes  and 
mounted  securely  on  a  light  brass  back — is  used  by  the  officers  of  the 
United  States  Signal  Service.  One  thermometer  is  lower  than  the 
other,  so  as  to  bring  the  bulbs  in  different  strata  of  air,  and  the  ap- 
paratus is  whirled  about  the  person  by  means  of  a  string.  When  wet, 
the  muslin-covered  bulb  will  fall  to  its  permanent  temperature  in 
about  two  minutes. 

A  School-room  Psychrometer. — The  pupil  may  make 
a  good  psychrometer  with  two  thermometers  which  read 
alike,  and  which  can  be  bought  for  less  than  a  dollar  apiece. 
Any  tinner  can  remove  some  of  the  metal  around  the  bulbs 
so  as  to  expose  them  similarly  and  permit  the  wrapping  of 
one  with  cloth.  Daily  observations  on  the  condition  of  the 
air  in  the  school-room  and  the  determination  of  the  dew- 
point  will  be  of  interest  to  the  pupils. 

The  Pressure  of  other  Vapors  corresponding  to  dif- 
ferent temperatures  has  been  carefully  measured.  In  the 
table  below,  the  values  for  four  are  given.  The  pressures 
are  in  centimetres  of  mercury,  and  the  temperatures  are  in 
Centigrade  degrees  : 
18 


266 


HEAT. 


T 

EMPERAT 

URES  CE 

NTIGRAD 

E. 

—  20°. 

0°. 

+  20°. 

40°. 

60°. 

80°. 

100°. 

Mercury  

0-002 

0-004 

0-008 

0-02 

0-04 

0-08 

Water  
Alcohol 

o-i 

0'3 

0'5 
1'3 

1-7 
4'5 

5-5 
13'4 

14-9 
35'1 

35-5 
81'3 

76-0 
169'5 

Ether  

6-8 

18-3 

43-3 

91-0 

172-9 

302-4 

495-1 

Any  liquid  boils  in  open  air  when  its  vapor  pressure 
equals  the  pressure  of  the  atmosphere.  The  bubbles  which 
form  in  the  liquid  then  pass  off  freely. 

In  the  table  above,  it  will  be  observed  that  at  100°  (the  boiling- 
point  of  water  in  open  air)  the  vapor  pressure  of  water  is  76  centime- 
tres (30  inches)  of  mercury.  The  vapor  of  alcohol  will  have  a  pressure 
of  76  centimetres  of  mercury  at  a  temperature  a  little  below  30°,  the 
pressure  at  80°  being  81'3.  The  boiling-point  of  alcohol  in  open  air 

is  therefore  a  little  below  80°. 
It  is  found  by  experiment  to  be 
78°.  Ether  vapors  have  a  press- 
ure of  91  centimetres  of  mer- 
cury at  40°.  The  boiling-point 
of  ether  is  therefore  below  40°. 
It  is  found  to  be  35°. 

Experiment  showing 
Vapor     Pressures.  —  If 

four  barometer-tubes  are 
filled  with  mercury,  the 
air  being  removed  as  com- 
pletely as  possible,  and  the 
open  ends  are  then  inserted 
in  a  vessel  of  mercury,  the 
space  above  the  mercury  in 
each  tube  will  be  a  Torri- 
cellian vacuum.  If  a  little 
water  be  now  introduced 
into  one  of  the  tubes  (B,  of 
Fig.  146),  it  will  instantly  vaporize  on  reaching  the  vacuum 
at  the  top.  The  column  will  also  be  depressed,  showing  that 


.  146.— VAPOR  PRESSURES. 


VAPOR  PRESS  LJHE8.  267 

the  vapor  presses  the  mercury  downward.  The  water  should 
be  added  in  small  quantities  until  the  top  of  the  column 
is  perceptibly  moist,  which  shows  that  the  vacuum  space 
has  been  saturated.  The  addition  of  more  water  would 
produce  no  further  depression  in  the  column,  except  such 
as  might  be  due  to  the  mere  weight  of  the  water. 

Introduce  alcohol  in  the  same  way  into  another  tube  (C)  and  the 
column  will  be  depressed  still  more.  Ether  in  a  third  tube  (D)  will 
cause  a  still  greater  depression.  If  the  temperature  of  the  mercury  in 
the  tubes  is  20°  C.,  which  is  a  common  temperature  in  school-rooms, 
and  if  all  the  air  is  removed  from  the  mercury  and  liquids,  the  col- 
umns into  which  the  three  liquids  were  introduced  will  be  depressed 
1-7,  4-5,  and  43'3  centimetres.  These  are  the  values  for  the  vapor 
pressures  at  20°  given  in  the  preceding  table.  The  fourth  barometer- 
tube  (A)  is  also  depressed  0-004  centimetre  by  the  mercury  vapor 
above  it.  This  amount  is  hardly  perceptible  to  the  unaided  eye. 

QUESTIONS.— What  is  the  source  of  atmospheric  vapor  ?  When  may  the  atmos- 
phere be  said  to  be  saturated  f  Explain  the  relation  between  saturation  and 
evaporation.  Define  humidity.  How  may  the  humidity  of  the  air  be  meas- 
ured ?  State  the  number  of  grains  to  a  cubic  foot  of  saturated  air  at  0°  Fahr.  ; 
at  80*.  What  does  the  difference  prove  ?  Explain  what  is  meant  by  the  dew- 
point.  If  the  air  is  cooled  below  the  dew-point,  what  takes  place  ?  Describe 
Regnaulfs  hygrometer,  for  determining  the  dew-point.  How  may  a  simpler 
apparatus  be  easily  constructed  ? 

What  is  meant  by  relative  humidity  ?  When  the  relative  humidity  is  low,  is  the 
air  moist  or  dry  ?  Is  discomfort  experienced  ?  State  a  reason  for  your  answer. 
Can  high  temperatures  be  better  borne  in  dry  or  saturated  air  ?  How  is  the 
relative  humidity  determined  by  the  officers  of  the  United  States  Geological 
Survey  ?  Is  it  possible  for  you  to  construct  a  fairly  accurate  psychrometer  ? 
How  would  you  determine  the  dew-point  from  the  readings  of  your  instru- 
ment ?  What  are  Glaisher's  factors  ?  Suppose  your  dry  bulb  to  read  26°  Fahr., 
and  your  wet  bulb  24'5*.  what  would  be  the  dew-point  ? 

When  may  a  liquid  be  said  to  boil  in  the  open  air  ?  What  is  the  vapor  pressure 
of  water  in  inches  of  mercury  at  100°  C.  ?  Of  alcohol  ?  Describe  an  experiment 
illustrating  the  vapor  pressure  of  water,  alcohol,  and  ether. 


SOME  SOURCES  OF  HEAT. 

Relation  between  Heat  and  Mechanical  Work. — 

Heat  may  be  produced  in  a  variety  of  ways  by  the  perform- 
ance of  work.  For  example,  a  metal  button  may  be  rubbed 
against  a  board  or  woolen  cloth,  as  shown  on  page  40. 


268  HEAT. 

The  force  required  to  make  the  button  slide  may  be  meas- 
ured in  pounds  weight  by  means  of  a  spring-balance,  and 
this  force,  multiplied  by  the  distance  in  feet  over  which  it 
is  exerted,  will  give  the  work  done  in  foot-pounds.  The 
button  will  quickly  become  warm,  and  if  dropped  into  water 
will  heat  it.  Some  of  the  heat  produced  is  lost  in  the  wood 
or  cloth,  which  also  becomes  warm. 

If  the  friction  is  continued,  the  metal  will  keep  warm 
indefinitely.  This  shows  that  heat  is  being  continually  pro- 
duced by  the  operation,  the  button  soon  cooling  to  the  tem- 
perature of  surrounding  bodies  when  the  friction  ceases. 

Friction    is    a    widely   known    Source    of   Heat. 

Even  savages  are  familiar  with  the  principle,  and  obtain 
fire  by  rubbing  together  pieces  of  dry  wood.  In  a  rapidly 
moving  railway  car,  the  heat  produced  by  the  friction  of 
the  axle  turning  in  the  box  sometimes  sets  fire  to  the  oily 
cotton-waste  contained  in  the  lubricating  chamber,  occa- 
sioning what  is  known  as  a  "  hot  box."  Ice  itself  may  be 
melted  by  forcibly  rubbing  two  pieces  together  at  a  tem- 
perature below  the  freezing-point. 

Count  Rumford  observed  that,  in  drilling  a  cannon,  the  metal  be- 
came very  hot.  He  surrounded  the  gun  by  a  box  containing  about  30 
pounds  of  water,  which  was  heated  to  the  boiling-point  in  two  hours 
and  a  half.  The  drill  was  driven  by  a  horse  working  on  a  capstan-bar. 
It  is  thus  evident  that  food  may  be  cooked  and  houses  heated  by  steam 
generated  by  the  work  of  horses.  But,  as  Count  Rumford  observed, 
this  would  never  pay,  since  more  heat  could  be  obtained  by  burning 
the  food  of  the  horse  than  from  his  work. 

Joule's  Determination  of  the  Mechanical  Equiva- 
lent of  Heat. — The  number  of  work  units  required  to  gen- 
erate one  heat  unit — i.  e.,  the  number  of  units  (foot-pounds) 
of  energy  equivalent  to  a  unit  quantity  of  heat — was  deter- 
mined experimentally  by  Joule  (jool).  He  employed  a  cop- 
per vessel,  B,  filled  with  water  and  provided  with  a  brass 
paddle-wheel,  arranged  somewhat  like  a  churn.  The  paddle 
was  driven  by  two  falling  weights,  E  and  F,  which  were 


MECHANICAL  EQUIVALENT  OF   HEAT. 


269 


suspended  from  rollers  connected  with  the  pulleys  C  and  D, 
provided  with  friction- wheels.  Cords  wound  on  these  pul- 
leys were  passed  around  the  vertical  paddle-shaft  A.  The 
two  weights  were  on  opposite  sides  of  the  churn,  in  order 

C 


FIG.  147.— APPARATUS  FOR  MEASUREMENT  OF  THE  MECHANICAL  EQUIVALENT 
OF  HEAT. 

to  avoid  friction  of  the  paddle-shaft  in  its  upper  bearing. 
When  the  weights  fell  and  the  paddle  revolved,  the  water 
was  heated  by  friction.  A  thermometer,  T,  indicated  its 
temperature  (see  Fig.  147). 

Various  liquids  were  tried,  and  it  was  found  that  for  every  heat 
unit  produced,  1,390  work  units  had  been  expended  on  the  liquid  by 
the  falling  weights,  which  were  wound  up  again  as  fast  as  they  reached 
the  ground.  The  heating  of  one  pound  of  water  through  one  degree 
Centigrade  is  mechanically  equivalent  to  the  lifting  of  1,390  pounds 
through  a  vertical  distance  of  one  foot,  or  of  one  pound  1,390  feet. 

A  laborer  can  perform  723.000  foot-pounds  of  work  in  ten  hours, 
thus  working  at  the  rate  of  20  foot-pounds  a  second.  If  such  a  work- 
man were  to  be  set  to  heating  water  by  turning  the  crank  of  Joule's 
apparatus,  he  would  produce  one  heat  unit  for  every  1,390  work  units 
in  a  day's  work.  In  ten  hours  he  would  generate  heat  enough  to  raise 
the  temperature  of  518  pounds  of  water  1°  C.  The  expense  of  heating 
water  by  this  method  would  be  enormously  greater  than  by  means  of 
burning  coal.  The  wages  of  the  laborer  would  be  at  least  one  dollar, 
while  the  coal  required  to  produce  513  heat  units  would  be  only  about 
one  ounce  (see  page  271). 


270  HEAT. 

The  total  daily  mechanical  and  heat  work  of  the  human  body  is 
estimated  at  7,216,000  foot-pounds,  which,  if  expended  in  lifting  the 
body,  would  raise  it  six  miles  against  gravity. 

Heat  produced  by  Collision.  —  If  a  bullet  from  a 
heavily  loaded  rifle  be  fired  into  dry  sand,  it  will  be  found 
to  have  become  hot,  or  even  fused.  A  rod  of  iron  can  quickly 
be  raised  to  a  red  heat  by  the  blows  of  a  steam-hammer,  and 
a  marked  rise  in  temperature  is  noticeable  in  lead  pounded 
on  an  anvil  (see  page  40).  Before  lucifer-matches  were  in- 
vented, the  blacksmith  used  to  ignite  sulphur  to  kindle  his 
forge-fire  with  a  nail  hammered  to  a  red  heat.  The  old 
flint-lock  gun  was  discharged  through  the  agency  of  heat 
evolved  by  the  striking  of  flint  and  steel  together  ;  the  heat 
ignited  the  particles  broken  off  by  the  blow,  producing 
sparks  which  fired  the  powder  in  the  pan. 

The  steam-hammer  and  the  rifle-ball  might  have  acquired 
the  velocity  with  which  they  strike  by  falling  in  a  vacuum 
from  a  certain  height,  and  the  work  which  is  done  in  the 
blow  of  either  may  be  measured  by  the  work  required  to  lift 
the  moving  body  in  question  to  this  height. 

A  rifle-ball,  for  instance,  would  acquire  a  velocity  of  1,500  feet  a 
second  by  falling  in  a  vacuum  through  a  distance  of  35,000  feet,  or 
over  6*5  miles.  If  the  ball  has  a  weight  of  -fa  pound,  and  strikes  with  a 
velocity  of  1,500  feet  a  second,  the  work  done  in  collision  is  35,000  x  -^, 
or  2,187  foot-pounds.  (See  the  example  on  page  99.)  Since  we  know 
by  Joule's  experiments  that  each  1,390  work  units  is  equivalent  to  one 
heat  unit,  the  heat  liberated  will  be  fif  £M  °r  1'57  heat  units.  If  we 
assume  that  half  the  heat  is  generated  in  the  lead,  the  other  half  being 
imparted  to  the  sand,  then  the  lead  will  receive  0'785  heat  unit.  How 
much  would  the  temperature  of  the  lead  rise? 

To  heat  one  pound  of  lead  1°  C.  requires  0*0314  heat  units  (see  page 

247).    To  heat  -fa  pound  1°  will  require  heat  units.    To  heat  the 

ball  t°  will  require  t.    This  must  equal  0-785  ;  hence 

'    .      16x0-785 


As  the  melting-point  of  lead  is  326,  it  is  clear  that  the  bullet  must 
fuse  before  its  temperature  is  raised  400  degrees. 


COMBUSTION. 


Such  experiments  as  that  just  described  help  to  explain 
the  nature  of  heat.  When  the  mass  in  motion  is  suddenly 
stopped,  the  molecules  of  the  body  are  thrown  into  vibra- 
tion (see  page  37).  Vibration  of  their  particles  may  thus 
be  induced  by  rubbing  bodies  together,  or  by  impact. 

Heat  due  to  Combustion. — When  carbon  burns,  the 
chemical  action  is  a  combination  of  the  carbon-particles  with 
oxygen-particles.  They  fall  together,  as  bodies  fall  to  the 
earth,  forming  carbon  dioxide  (carbonic  acid  gas).  It  is 
found  that  the  complete  combustion  of  a  pound  of  char- 
coal to  carbon  dioxide  produces  8,080  heat  units,  or  enough 
to  heat  8,080  pounds  of  water  1°  C.  Since  one  heat  unit  is 
equivalent  to  1,390  work  units,  the  heat  produced  by  the 
combustion  of  one  pound  of  coal  is  equivalent  to  8,080  X 
1,390  =  11,231,000  work  units. 

If  the  pound  of  coal  should  fall  through  the  distance  of 
11,231,000  feet,  or  2,127  miles,  with  the  acceleration  which 
it  has  at  the  earth's  surface,  the  heat  produced  on  striking 
would  be  equal  to  that  evolved  by  the  burning  of  a  pound 
of  coal.  The  same  heat  would  be  produced  by  the  falling 
of  100  tons  of  2,000  pounds  each  through  56  feet. 

The  following  table  gives  the  heat  produced  by  the  burning  of  a 
pound  of  various  substances,  and  in  the  third  column  is  stated  the 
distance  through  which  100  tons  must  fall  to  yield  the  same  heat : 


SUBSTANCE. 

Heat 
units. 

Fall  in 
feet  of 
100  tons. 

SUBSTANCE. 

Heat 
unit*. 

Fall  in 
feet  of 
100  tons. 

Hydrogen  

34,462 

240 

Coke    

7,000 

49 

Anthracite 

8460 

59 

Dry  wood 

4025 

28 

Charcoal  

8,080 

56 

Moist  wood  

3,100 

22 

Good  bituminous  coal 

8000 

56 

Iron         

1,576 

11 

As  in  the  operation  of  boiling,  these  combustions  go  on  in  air  at 
definite  temperatures.  The  bodies  must  be  raised  to  the  proper  tem- 
perature before  combustion  takes  place  freely.  The  temperature  at 
which  iron  will  take  fire  and  burn  in  air  is  higher  than  that  necessary 
for  charcoal. 


HEAT. 


The  Heating1  Power  of  Coal,  or  of  any  other  combus- 
tible solid,  may  be  determined  by  means  of  the  calorimeter 
shown  in  Fig.  148. 

The  coal,  mingled  with  a  fuel  mixture,  is  tightly  packed  in  a  cylin- 
der of  heavy  copper,  C,  having  a  length  of  four  inches  and  a  diameter 
of  f  to  |  inch.  This  cylinder  is  supported  in  a  socket  soldered  to  the 
bed-piece  D.  An  outer  cylinder,  A,  about  5f  inches  long  and  2  inches 
in  diameter,  sets  down  over  the  fuel  cylinder,  and  locks  to  the  bed-plate 
as  the  bottom  of  a  lantern  locks  to  the  globe.  Four  brass  springs  Gr 
serve  to  guide  the  cylinder  A  to  its  place,  in  order  that  the  parts  may 

be  quickly  fastened  together. 
The  fuse  /  is  ignited,  and,  be- 
fore the  fuel  begins  to  burn,  the 
cylinder  is  locked  in  position  and 
the  whole  apparatus  is  plunged 
under  a  weighed  amount  of 
water  in  the  copper  vessel  B. 

The  upper  cock  being  closed, 
no  water  can  enter  the  cylinder 
A  except  a  little  at  the  bottom 
through  the  small  holes  h. 
Through  these  holes,  the  hot 
gases  formed  by  the  combustion 
issue,  and  rise  in  bubbles  through 
the  cooling  water.  After  the 
combustion  has  ceased,  the  cock 
is  opened  at  the  top,  and  water 

rises  and  fills  the  whole  apparatus.  This  should  be  blown  out  and 
mixed  with  the  external  water,  in  order  to  secure  a  uniform  tempera- 
ture. The  temperature  of  the  water  having  been  read  just  before  the 
operation,  and  subsequently  at  its  close,  the  amount  of  heat  liberated 
by  the  combustion  is  readily  ascertained. 

The  fuel  mixture  consists  of  three  parts  by  weight  of  potassium 
chlorate  mixed  with  one  part  of  niter.  These  substances  should  be  in 
powdered  form,  dry,  and  thoroughly  mixed.  The  mixture  must  be 
handled  with  some  care.  For  each  part  of  pulverized  coal,  about  ten 
parts  of  the  fuel  mixture  are  required.  Not  over  three  grammes  of 
coal  can  be  used  at  one  charge,  and  this  should  be  tightly  packed  to 
prevent  too  rapid  combustion. 

The  fuse  is  a  narrow  strip  of  blotting-paper,  which  has  been  dipped 
£wo  or  three  times  in  a  solution  of  potassium  chlorate.  Clamp  the  fuse. 


Fio.  148. — SECTION  OF 
CALORIMETER. 


ANIMAL  HEAT.  273 

midway  in  a  pair  of  pliers  or  a  vise,  and  burn  off  the  external  coating 
of  the  salt  from  one  end.  Insert  the  unburned  end  into  the  charge. 
The  fuse  will  burn  slowly  down  to  the  part  still  coated  with  the  salt, 
and  thus  give  time  to  place  the  furnace  in  position  under  water.  On 
a  damp  day,  the  fuse  is  likely  to  fail  unless  gently  warmed. 

For  lecture  purposes,  the  outer  vessel  B  may  be  of  glass, 
so  that  the  operation  may  be  seen.  The  experiment  is  a 
most  impressive  one. 

If  the  whole  apparatus,  including  the  vessel  B,  weighs 
1,260  grammes,  the  heat  required  to  raise  its  temperature 
1°  C.  (as  it  is  of  copper)  will  be  1,260  X  0-0952,  or  120  heat 
units.  If  the  vessel  contain  3,000  grammes  of  water,  then 
for  each  degree  of  rise  in  temperature  the  heat  required 
would  be  3,120  heat  units. 

A  correction  should:  yet  be  made  for  the  heat  generated  by  the 
fuse.  This  is  best  done  by  tearing  four  or  five  fuses  to  shreds,  and 
packing  them  in  a  charge.  The  additional  heat  produced  will  be  due 
to  them,  and  the  amount  due  to  one  can  readily  be  found. 

Animal  Heat. — In  all  the  organs  of  animals,  oxidation, 
or  burning  of  organic  matter  derived  from  food,  is  going  on. 
The  oxygen  is  taken  into  the  blood  through  the  lungs,  and 
is  evenly  distributed  to  all  parts  of  the  body.  When  an  ani- 
mal is  at  work,  it  requires  more  of  this  oxygen,  and  hence 
breathes  faster  and  consumes  more  of  the  organic  tissue  than 
when  at  rest.  The  chemical  products  of  the  oxidation  tak- 
ing place  in  the  body,  like  those  of  ordinary  combustion,  are 
carbon  dioxide  and  water,  which  pass  off  in  part  in  the 
breath  and  through  the  skin.  It  is  this  oxidation  that  pro- 
duces the  heat  of  the  body. 

In  the  severe  cold  of  arctic  regions,  life  consists  largely  in  an 
effort  to  eat  and  digest  food  enough  to  maintain  the  normal  tempera- 
ture. The  Eskimos  sustain  their  vital  heat  by  a  diet  of  fish-oil  and 
seal's  blubber,  greasy  food  being  rich  in  carbon. 

In  all  animals  in  a  state  of  health,  the  heat-producing 
and  heat-destroying  processes  balance  each  other,  and  hence 


•274  HEAT. 

a  standard  temperature  is  maintained — but  this  standard 
differs  in  different  species.  Birds  and  mammals,  having  a 
high  vital  heat,  are  classed  as  "  warm-blooded  animals."  The 
mean  temperature  of  some  birds  is  above  111°  Fahr.  The 
standard  in  man  is  98*6°,  and  any  deviation  from  this  stand- 
ard is  regarded  as  a  sign  of  disease  ;  temperatures  below  97° 
Fahr.  or  above  106°  Fahr.  are  extremely  dangerous  to  life. 
Exposed  parts,  however,  such  as  ears  and  fingers,  are  con- 
stantly cooled  below  the  normal  temperature  of  the  blood 
and  internal  organs.  Eeptiles  and  fishes  have  low  bodily 
temperatures,  and  are  hence  called  "  cold-blooded." 

LAVOISIER'S  EXPERIMENT. — Lavoisier  (lah-vwah-ze-ay1)  imprisoned 
a  guinea-pig  in  a  box  surrounded  by  ice,  placing  the  box  in  a  room 
at  the  freezing-point.  The  heat  of  the  animal's  body  fused  402*27 
grammes  (0'887  pound)  in  ten  hours.  To  fuse  one  pound  of  ice  re- 
quires 79  heat  units ;  hence  the  animal  produced  79  x  0'887  =  70  heat 
units  in  ten  hours.  This  would  be  equivalent  to  1,390x70  work 
units,  or  97,300  foot-pounds.  The  guinea-pig  weighed  four  pounds. 
If  the  work  had  been  employed  in  lifting  him,  it  would  have 
raised  him  through  aif Qa  =  24,325  feet,  or  4-6  miles  in  ten  hours. 
Ten  hours  =  36,000  seconds.  Hence  the  work  performed  in  each 
second  would  have  lifted  the  animal's  body  flffo  =  0-67  foot,  or  about 
8  inches. 

Plant  Temperature. — It  has  long  been  known  that 
plants  evolve  heat  in  connection  with  flowering,  and  this 
heat  has  been  found  to  depend  on  the  chemical  processes 
which  take  place  within  the  plant,  transforming  the  matters 
derived  from  the  soil  into  starch,  sugar,  and  other  products. 
By  placing  the  bulb  of  a  thermometer  in  contact  with  blos- 
soms of  Arum  under  a  bell- jar,  it  has  been  established,  not 
only  that  they  have  a  temperature  higher  than  that  of  the 
air,  but  also  that  the  evolution  of  heat  is  variable.  At  3 
p.  M.,  the  air  temperature  being  15'6°  C.,  the  temperature  of 
the  flowers  was  observed  to  be  16-1°  C. ;  at  5.45  and  6.15 
p.  M.,  when  the  air  temperature  had  fallen  to  15°,  the  ther- 
mometer in  contact  with  the  flowers  recorded  respectively 
19-8°  and  21°. 


HEAT  BY  COMPRESSION.  275 

A  liquid  in  which  the  yeast-plant  is  growing,  acquires  a  tempera- 
ture above  that  of  the  air.  The  same  is  true  of  germinating  seeds,  as 
illustrated  in  the  malting  of  barley.  Corn  in  the  act  of  germination 
rises  in  temperature  from  6'25°  to  7'5°  C.  above  the  air ;  clover,  17'5°  C. 

Plants  sometimes  have  a  temperature  lower  than  that  of  the  air, 
and  hence  may  suffer  from  frost  when  the  temperature  of  the  air  is 
above  freezing.  The  mean  temperature  of  the  trunks  of  trees  is  found 
to  be  higher  than  that  of  the  air  in  autumn  and  winter,  and  lower  in 
spring  and  summer. 

Heat  by  Compression. — When  a  body,  which  expands 
when  heat  is  applied  to  it,  is  compressed,  it  becomes  hot,  and 
gives  off  heat  to  surrounding  bodies.  Bodies  which  con- 
tract on  being  heated,  become  cool  when  compressed. 

By  violent  and  quick  compression,  enough  heat  can  be  set  free 
from  air  to  ignite  tinder.  This  is  done  with  the  Pneumatic  Syringe, 
consisting  of  a  glass  barrel  and  tightly  fitting  piston  (see  Fig.  107, 
page  205).  In  the  extremity  of  the  piston  is  a  small  cavity,  in  which 
some  tinder  is  placed.  When  the  piston  is  driven  rapidly  down,  the 
air  in  the  barrel  is  compressed,  muscular  energy  is  transformed  into 
heat,  and  the  tinder  is  set  on  fire. 

QUESTIONS.— How  may  heat  be  produced  by  the  application  of  work  ?  What  is 
Friction  ?  Explain  the  heat  of  friction.  State  some  familiar  instances  in  which 
heat  is  produced  by  friction.  How  do  savages  kindle  fires  ?  How  great  a  heat 
has  been  produced  by  boring  a  cannon  ?  Explain  Joule's  method  for  determin- 
ing the  mechanical  equivalent  of  heat.  How  many  work  units  were  found  to 
be  equivalent  to  a  heat  unit  ?  Give  some  familiar  examples  of  the  production 
of  heat  by  collision  or  percussion.  How  does  a  rifle-ball  acquire  the  velocity 
with  which  it  strikes,  and  how  may  the  work  implied  in  its  blow  be  measured  ? 
Suppose  an  ounce  bullet  of  lead  to  acquire  a  velocity  of  1,500  feet  a  second  by 
falling  through  a  distance  of  35,000  feet ;  what  will  be  its  rise  in  temperature 
when  it  strikes  the  ground  ?  Does  this  imply  that  the  lead  ball  may  fuse  ? 

Describe  the  combination  of  elements  that  occurs  in  the  combustion  of  coal. 
Give  the  value  in  work  units  of  the  heat  produced  by  the  combustion  of  a  pound 
of  coal.  Describe  the  apparatus  and  the  process  by  which  the  heating  power 
of  coal  may  be  determined.  What  is  Animal  Heat,  and  to  what  is  it  attribu- 
table ?  Compare  the  chemical  changes  taking  place  in  the  living  body  with 
ordinary  combustion.  How  is  animal  heat  sustained  amid  arctic  cold  ?  Why 
are  not  meat  and  greasy  food  an  appropriate  diet  for  summer  ?  Explain  why  a 
standard  temperature  is  maintained  in  all  animals.  What  is  said  of  animal 
heat  in  different  species  ?  State  the  normal  temperature  in  man,  and  devia- 
tions that  are  dangerous.  The  mean  temperature  of  birds. 

Narrate  the  results  of  Lavoisier^s  experiment  in  regard  to  animal  heat.  What 
has  long  been  known  in  connection  with  plants  ?  On  what  does  the  heat  of 
plants  depend  ?  Do  plants  ever  have  a  temperature  lower  than  that  of  the  air  ? 
Illustrate.  What  can  you  say  of  compression  as  a  source  of  heat  ? 


276  HEAT. 


DIFFUSION  OF  HEAT. 

Heat  always  tends  to  pass  from  warmer  to  colder 
bodies.  If  several  bodies  near  one  another  have  different 
temperatures,  those  that  are  hot  become  colder,  and  those 
that  are  cold  become  warmer,  until  all  have  a  common 
temperature.  If  all  bodies  had  the  same  temperature,  we 
should  know  nothing  of  heat.  This  equalizing  of  tempera- 
tures is  brought  about  in  three  ways,  viz.,  by  Conduction, 
by  Convection,  and  by  Radiation. 

Conduction. — Thrust  one  end  of  a  pin  into  a  gas-flame. 
It  will  quickly  become  too  hot  to  be  held  in  the  hand.  The 
heat  enters  the  metal  pin  at  the  end  kept  in  the  flame,  and 
is  transmitted  along  its  whole  length.  A  splinter  of  wood, 
a  roll  of  paper,  a  glass  tube,  or  a  platinum  wire,  may  be 
held  with  comfort  by  one  end  while  the  other  is  burning  or 
fusing.  The  brass  pin  is  said  to  be  a  letter  conductor  than 
the  glass  tube  or  platinum  wire. 

Among  metals,  silver,  copper,  and  gold,  are  examples  of  good  con- 
ductors ;  while  bismuth,  German  silver,  and  platinum,  are  bad  con- 
ductors. You  can  understand  why  articles  made  of  certain  metals 
feel  intensely  cold  in  winter.  It  is  because  they  conduct  the  heat  of 
the  hand  rapidly  away. 

The  principle  upon  which  heat  is  conveyed  by  conduc- 
tion is  that  of  communication  from  particle  to  particle  of 
the  body  receiving  it.  As  each  particle  is  set  in  more  vio- 
lent motion,  it  imparts  this  motion  to  the  more  slowly  mov- 
ing particles  next  to  it,  these  to  others,  and  so  on,  until  those 
farthest  from  the  source  of  heat  are  reached. 

The  relative  conducting  powers  of  some  of  the  more  common  metals  are  here 
given,  that  of  silver  being  taken  as  100  : 

Silver  .        .        .       '.'•".'      .  100  Steel.  .       .       .       .       ,       .  12 

Copper .  74  Lead  .  .       .       ...        .  9 

Gold  ......  53  Platinum  ......  8 

Tin   .  .....  15  Bismuth  .,,,,.  9 


CONDUCTION. 


277 


The  Principle  of  Conduction  applied  to  Clothing. 

— When  heat  is  being  drawn  rapidly  from  our  bodies,  the 
sensation  of  cold  is  produced.  Bad  conductors  should,  there- 
fore, be  chosen  for  clothing  materials,  that  the  animal  heat 
may  be  retained  about  the  body  and  dangerous  chilling  pre- 
vented. Wool  and  silk  meet  this  condition  perfectly,  and 
cotton  is  to  a  certain  extent  safe ;  but  linen  is  a  good  con- 
ductor, and  should  never  be  worn  next  the  skin,  as  it  cools 
the  body  too  rapidly  in  perspiration. 

Hair  is  a  bad  conductor,  and,  hence  is  an  equally  good  protector 
against  heat  and  cold.  Explorers,  in  tropical  as  well  as  arctic  re- 
gions, allow  the  hair  and  beard  to  grow.  On  the  approach  of  winter, 
Nature  provides  for  the  protection  of  the  lower  animals  by  a  heavy 
growth  of  hair,  wool,  or  feathers,  and  by  a  jacket  of  fat,  which  is  also 
a  non-conductor. 

Conduction  in  Liquids. — Liquids,  as  a  rule,  are  poorer 
conductors  than  most  solids.     Fill  a  test-tube  with  water,  as 
shown  in  Fig.  150,  place  a  fragment  of  ice  at  the  bottom, 
and  hold  it  down  with 
a  glass  rod.     If  a  flame 
now   be    applied    near 
the  surface,  the  water 
there   may   be    boiled, 
while  the  ice,  surround- 
ed by  the  denser  cold 
water    below,    remains 
unfused  at  the  bottom. 
If  the  ice  be  allowed  to 
float  to  the  top  of  the 
tube,  the  heat  being  ap- 
plied at  the  bottom,  the 
heated  water  will   rise          F^  150.-WATER  A  NON-CONDUCTOR. 
to  the  top  and  the  cool 

water  from  the  ice  will  descend.  This  mixture  of  the  cold 
and  hot  particles  will  prevent  the  water  from  boiling  until 
the  ice  has  fused. 


HEAT. 


Fig.  151  also  shows  a  method  of  testing  the  conducting  power  of 
liquids.  The  stem  of  an  air  thermometer  passes  through  a  cork  fitted 

into  the  neck  of  a  glass  funnel.  The 
lower  end  of  the  stem  dips  into  a  ves- 
sel of  water.  Fill  the  funnel  with 
water  so  that  the  bulb  is  covered  to 
the  depth  of  half  an  inch.  Pour  a 
little  ether  upon  the  water  in  the  fun- 
nel and  ignite  it  (after  having  stop- 
pered and  removed  the  ether-bottle). 
While  the  surface  of  the  water  is  con- 
siderably heated,  the  thermometer  will 
be  but  slightly  affected.  This  shows 
that  heat  penetrates  water  by  conduc- 
tion very  slowly. 

It  is  doubtful  whether  gases 
have  any  true  conducting  power. 
The  difficulty  of  studying  this 
point  arises  from  the  impossi- 
bility of  preventing  the  heating 
of  the  gas  by  convection,  the 
next  method  of  diffusion  to  be 
discussed.  It  is  partly  because 

their  interstices,  are  filled  with  air,  that  woolen  fabrics  are 

poor  conductors. 

Snow  is  a  bad  Conductor,  and  hence  is  popularly 
said  to  keep  the  earth  warm.  Its  flakes  are  formed  of  crys- 
tals, which  collect  into  feathery  masses,  imprisoning  air, 


FIG.  151.— AIR  THERMOMETER  IN 
FUNNEL  OP  WATER. 


FIG.  152.— TYPES  OF  SNOW-CRYSTALS. 


and  thus  interfere  with  the  escape  of  heat  from  the  earth's 
surface.  The  winter  dwellings  of  the  Eskimos  are  shielded 
from  the  cold  by  their  snow  covering.  Hunters  surprised 


RADIATION   OF   HEAT.  279 

by  night  in  the  forest  dig  holes  in  the  snow  for  protection, 
and  the  instinct  of  certain  animals  leads  them  to  take  ad- 
vantage of  the  same  shelter.  A  covey  of  grouse  will  dash 
into  a  snow-bank,  and  remain  there  in  safety  when  the  out- 
side temperature  is  dangerous  to  life. 

Convection. — Liquids  and  gases  are  heated  mainly  by 
Convection,  or  transmission  by  means  of  currents.  The  air 
immediately  in  contact  with  a  hot  stove,  being  heated  and 
thereby  made  less  dense,  ascends,  and  is  replaced  by  colder 
and  denser  air  from  below.  The  warm  column  rises  to  the 
upper  part  of  the  room,  and  then,  descending  beside  the 
walls,  loses  part  of  its  heat  and  approaches  the  stove  again 
along  the  floor. 

Similar  currents  are  produced  in  a  test-tube  or  tall  beaker  of  water 
when  heated  over  the  flame  of  a  spirit-lamp.  The  currents  can  be 
made  apparent  by  placing  a  little  bran  or  sawdust  in  the  water. 

Radiation  of  Heat. — If  we  stand  in  front  of  a  fire  or 
hot  stove,  we  experience  a  feeling  of  warmth.  This  is  not 
due  to  the  fact  that  the  air  in  contact  with  us  is  warm, 
since  if  a  screen  be  interposed  the  heat  ceases  to  be  felt. 
Such  transmission  of  heat  is  known  as  Eadiation. 

The  pupil  must  understand,  in  this  connection,  that  the  heat  of 
the  radiating  body  is  wholly  transformed,  at  the  instant  of  radiation, 
into  Radiant  Energy  (see  pages  38  and  293).  Throughout  the  space 
between  the  radiating  and  receiving  object,  the  radiation  is  a  form  of 
energy  entirely  distinct  from  heat.  The  heat  of  the  open  fire,  for  ex- 
ample, transformed  into  radiant  energy  as  just  stated,  passes  on  to  us 
as  radiant  energy,  and  is  retransformed  into  heat  when  it  strikes  our 
bodies.  Radiation,  therefore,  strictly  speaking,  is  the  transmission  of 
radiant  energy,  and  not  of  heat.  For  the  sake  of  brevity,  we  speak  of 
heat  radiation. 

The  Power  of  radiating  Heat  varies  in  different  bod- 
ies. Lamp-black,  paper,  and  glass,  are  good  radiators ;  pol- 
ished tin  and  silver,  the  reverse ;  but  any  metal  that  is 
painted  becomes  an  excellent  radiator.  Water  will  remain 
hot  a  longer  time  in  a  smooth  silver  cup  than  in  a  china 


280  HEAT. 

one,  provided  neither  is  in  contact  with  a  conductor.  The 
hearth-stone,  when  the  fire  is  lighted,  receives  heat  abund- 
antly from  the  blazing  fuel  and  radiates  it  freely  to  the  sur- 
rounding air.  Why  does  the  hearth-stone  now  feel  warmer 
to  the  bare  foot  than  the  rug? 

Good  radiators  are  also  good  absorbers,  and  vice  versa.  The  bot- 
tom of  the  tea-kettle  is  allowed  to  remain  thinly  coated  with  soot  to 
counteract  the  non-absorbing  property  of  the  bright  new  surface.  A 
very  thin  film  of  metal  interferes  with  radiation  and  absorption.  The 
Chinese  are  aware  of  this,  and  gild  their  silk  umbrellas  to  keep  out  the 
heat  of  the  sun. 

Radiation  in  a  Vacuum. — If  a  thermometer  be  sealed 
into  a  glass  globe,  the  mercury-bulb  being  at  the  center  of 
the  globe,  and  if  the  globe  be  then  exhausted 
as  completely  as  possible,  heat  will  nevertheless 
affect  the  thermometer  even  better  than  when 
the  globe  is  filled  with  air. 

This  may  be  shown  (Fig.  153)  by  dipping  the  globe 
into  hot  water.    The  thermometer  will  at  once  rise. 
A  hot  cloth  wrapped  around  the  thermometer  stem, 
outside  the  bulb,  will  not  appreciably  affect  the  instru- 
„     ._„    T          nient;  but,  if  the  cloth  be  wrapped  around  the  globe, 
MOMETER  IN  A    a  rise  will  instantly  be  observed.     This  shows  that 
VACUUM.  the  heat  is  radiated  from  the  sides  of  the  globe  to 

the  thermometer-bulb,  and  is  not  conducted  along  the 
stem.  Solar  heat  may  be  concentrated  upon  the  bulb  by  means  of  a 
lens ;  light  and  heat  will  both  traverse  the  so-called  vacuum. 

The  heat  which  comes  to  us  from  the  sun  passes  through  the  inter- 
planetary space,  which  is  substantially  a  vacuum  (see  page  293). 

Law  of  Distance. — A  hot  ball  of  metal  transmits  heat 
in  all  directions,  and  will  cool  unless  continually  supplied 
with  heat.  A  certain  amount  of  heat  leaves  the  ball  during 
each  second.  Imagine  a  spherical  concentric  surface  sur- 
rounding the  ball,  its  radius  being  three  feet  (Fig.  154). 
All  the  heat  which  leaves  the  ball  each  second  will  pass 
through  this  surface  each  second,  if  the  intervening  medi- 
um is  not  heated. 


LAWS  OF  DISTANCE  AND  COOLING. 


281 


FIG.  154.— LAW  OF  DISTANCE. 


If  we  imagine  a  second  concentric  spherical  surface,  having  twice 
the  radius  of  the  former,  the  heat  which  passes  through  the  first  sur- 
face every  second  would  also  pass 
through  the  larger  surface  in  the  same 
time.  But  the  outer  surface  has  four 
times  the  area  of  the  inner,  since,  by 
a  geometrical  law,  the  surfaces  of 
spheres  are  as  the  squares  of  their 
radii.  The  heat  which  would  fall 
upon  a  unit  area  of  the  inner  surface 
would  therefore  spread  over  four  units 
of  area  at  twice  the  distance,  nine 
units  of  area  at  three  times  the  dis- 
tance, etc.  Hence  the  heat  per  unit 
area  at  distances  1,  2,  3,  4,  will  be  in 
the  ratio  of  1,  ±,  ^,  -fa  etc. 

The  heating  effect  of  a  small  radiant  mass  upon  a  distant  object 
would  thus  vary  inversely  as  the  square  of  the  distance.  A  similar 
law  applies  in  the  case  of  light  and  sound  radiated  from  a  point. 

Law  of  Cooling. — A  hot  body  surrounded  by  cooler 
bodies  radiates  its  heat  and  cools  down  to  the  temperature 
of  its  surroundings.  When  the  difference  in  temperature 
is  not  over  ten  degrees,  the  heat  radiated  per  minute  (and 
therefore  the  fall  in  temperature  per  minute)  is  very  nearly 
proportional  to  the  difference  in  temperature  between  the 
hot  body  and  the  surrounding  bodies. 

When  a  body  is  exposed  to  any  source  of  heat,  it  rises  in 
temperature,  but  at  the  same  time  it  begins  to  radiate  more 
heat.  It  will  finally  reach  a  temperature  at  which  the 
amount  of  heat  radiated  per  second  will  equal  that  received 
in  a  second.  Its  temperature  will  then  cease  to  rise. 

In  winter,  heat  radiates  from  the  human  body  more  rapidly  than 
in  summer,  because  the  difference  in  temperature  between  the  body 
and  the  surrounding  air  is  then  great.  In  the  arctic  regions,  the  drain 
upon  the  animal  heat  of  the  body  is  very  severe,  and  a  large  part  of 
the  energy  of  the  inhabitants  is  expended  in  keeping  themselves 
warm  (see  page  273). 

In  the  torrid  zone  also,  radiation  plays  an  important  part.  The 
heat  of  the  body  is  not  so  rapidly  radiated  as  in  temperate  regions. 
19 


282  HEAT. 

The  inhabitants,  therefore,  live  on  light  vegetable  foods,  and  are  slug- 
gish and  indolent  in  their  habits,  in  order  to  avoid  overheating. 

QUESTIONS.— What  is  meant  by  the  diffusion  of  heat  ?  Explain  what  takes  place 
when  several  bodies  having  different  temperatures  are  brought  near  one  an- 
other. By  what  three  processes  are  temperatures  equalized  ?  Describe  the 
principle  and  effects  of  Conduction.  Mention  some  poor  conductors ;  some 
good  conductors.  Explain  why  certain  metallic  articles  feel  intensely  cold  in 
winter.  Why  are  cooking  utensils  provided  with  wooden  handles  ?  Are  stone 
and  marble  good  conductors  ?  Prove  it.  What  lesson  may  you  learn  from  this  ? 
Fire-brick  is  a  bad  conductor  :  why  are  stoves  and  furnaces  lined  with  it  ? 
What  can  you  say  of  the  relative  value  of  materials  used  for  clothing  ?  Why  is 
an  eider-down  quilt  incomparable  as  a  cover  at  night  ?  What  is  the  value  of 
hair  ?  How  does  Nature  protect  the  lower  animals  from  cold  ?  Do  you  think 
the  bark  of  a  tree  fulfills  any  such  purpose  ?  Do  fur  garments  impart  heat  to 
the  body  ?  Why  is  flannel  used  to  wrap  ice  in  summer  ? 

Which  are  the  better  conductors  of  heat— liquids  or  solids  ?  Liquids  or  gases  ? 
Prove  that  water  is  an  imperfect  conductor.  Illustrate  the  non-conducting 
property  of  snow.  Did  you  ever  notice  in  a  building  heated  with  steam  that 
the  pipes  are  wrapped  with  asbestos  or  felt  and  covered  with  canvas  ?  Why  is 
this  ?  Describe  Convection  ;  how  may  it  be  illustrated  ? 

Explain  Radiation.  Of  what  is  it  really  the  transmission  ?  Exactly  how  is  heat 
communicated  from  hot  objects  to  our  bodies  ?  What  is  Radiant  Energy  ? 
Show  how  the  power  of  radiating  heat  varies  in  different  bodies.  What  is  the 
relation  between  radiation  and  absorption  ?  The  conducting  pipes  in  steam- 
engines  are  never  painted  ;  why  ?  Prove  that  radiation  takes  place  in  a  so- 
called  vacuum.  State  the  law  of  distance  in  regard  to  radiation  ?  How  does 
heating  effect  vary  ?  When  does  the  temperature  of  a  body  exposed  to  heat 
cease  to  rise  ?  Demonstrate  the  law  of  cooling,  and  apply  it  in  the  case  of 
radiation  from  the  human  body  in  winter. 

ISOTHERMS  AND  ISOTHERMAL  SURFACES. 

Isothermal  Lines. — If  at  any  time  the  temperature  of 
the  air  were  observed  over  the  whole  surface  of  the  earth, 
and  the  temperatures  taken  were  recorded  on  a  globe  or  map 
of  the  world,  each  in  its  proper  place,  there  would  result  a 
series  of  places  in  both  the  northern  and  the  southern  hemi- 
sphere at  which  the  temperature  would  be  70°  Fahr.  Lines 
connecting  these  points  would  coincide  roughly  with  paral- 
lels of  latitude.  Between  these  two  lines,  in  a  belt  covering 
the  equatorial  regions,  the  temperatures  would  be  above  70°, 
while  for  points  nearer  the  poles  the  temperatures  would  be 
lower.  A  line  connecting  a  series  of  places  whose  mean 
temperature  is  the  same  is  called  an  isotherm,  or  line  of 
equal  temperature. 


£££   ISOTHERMAL   SURFACES.  283 

The  position  of  isothermal  lines  is  continually  changing.  If  a 
thermometer  which  now  reads  70°  should  in  a  few  hours  read  80°,  it 
would  show  that  the  isotherm  of  70°  had  moved  to  a  higher  latitude. 
It  often  happens  that  when  it  is  growing  warmer  in  New  York,  it  is 
growing  colder  in  Ohio,  and  vice  versa.  At  points  on  the  earth  where 
day  is  dawning,  these  lines  are  generally  moving  away  from  the  equa- 
torial regions ;  while  180°  distant,  where  evening  is  coming  on,  the 
lines  are  moving  toward  the  equator.  These  general  movements  are 
modified  by  storms  and  air-currents,  so  that  the  lines  are  continually 
shifting  to  and  fro  in  a  very  irregular  manner. 

Isothermal  Surfaces. — Suppose  the  temperature  of  the 
air  at  the  earth's  surface  is  found  to  be  70°  at  some  station. 
If  the  thermometer  is  carried  up  into  the  air,  from  this 
station,  it  will  generally  show  a  colder  temperature.  At  the 
height  of  1,000  feet,  it  would  have  to  be  moved  toward  the 
equator  in  order  to  register  again  a  temperature  of  70°.  If 
we  suppose  the  thermometer  to  continue  to  ascend,  while 
at  the  same  time  moving  southward  in  order  that  a  tempera- 
ture of  70°  may  be  maintained,  we  imply  that  it  ultimately 
reaches  the  equator.  If  the  southward  direction  is  still  con- 
tinued, it  will  be  necessary  to  approach  the  surface  of  the 
earth  in  order  to  maintain  a  constant  temperature  of  70°, 
and  we  shall  finally  reach  it  at  the  southern  isotherm  of  70°. 

A  thermometer  might  thus  be  carried  from  any  point  on 
the  northern  isotherm  due  south,  in  some  such  path  as  that 
described,  and  finally  reach  the  southern  isotherm,  indicat- 
ing at  all  points  on  the  route  a  temperature  of  70°. 

If  the  journey  were  conducted  a  few  feet  below  the  surface  of  the 
earth,  the  temperature  would  fall ;  but,  toward  the  equator,  we  should 
find  the  soil  warmer.  A  subterranean  path  connecting  the  two  iso- 
therms might  be  found,  where  the  temperature  is  70°.  This  path 
would  lie  near  the  surface,  but  somewhat  deeper  at  the  equator  than 
at  higher  latitudes. 

Clearly,  then,  we  have  here  an  isothermal  surface,  surrounding  the 
earth  at  its  equatorial  region,  and  having  a  shape  somewhat  like  that 
often  given  to  a  finger-ring  (Fig.  155).  This  surface  is  continually 
fluctuated  into  irregular  billows,  by  clouds,  storms,  and  currents  of  air. 
The  isothermal  lines  drawn  in  physical  geographies  are  the  lines  in 


284 


HEAT. 


which  isothermal  surfaces  intersect  the  surface  of  the  earth.  (See  Ap- 
pletons'  Physical  Geography,  pages  66,  67.) 

Isothermal    Surfaces    within    the    Earth.  —  If    we 

should  start  with  a  thermometer  at  the  surface  of  the  earth, 
within  the  equatorial  ring  of  70°,  and  carry  it  downward  a 
few  inches  or  feet  into  the  soil,  the  temperature  would  fall, 
perhaps  to  70°.  While  descending  through  twenty  or  thirty 
feet,  the  temperature  would  continue  to  fall,  but  thereafter 
it  would  rise,  as  we  approach  the  hot  interior  of  the  earth. 

COLD  -20° 


COLD 

FIG.  155.— ISOTHERMAL  SURFACES. 

At  a  depth  of  perhaps  800  feet,  the  temperature  would 
have  risen  to  70°  again.  Here  we  are  on  another  isotherm 
of  70°,  surrounding  the  interior  hot  core  of  the  earth.  This 
surface  is  probably  wholly  within  the  earth,  excepting  where 
it  may  be  carried  up  by  a  hot  spring  or  volcano.  Within 
this  isotherm  will  be  others,  having  higher  temperatures. 

Isotherm  of  —  2O°  Fahr. — In  the  equatorial  region  of 
the  earth,  a  temperature  of  —20°  would  never  occur,  either 
at  or  below  the  earth's  surface.  In  the  arctic  regions,  the 
air  falls  far  below  this  temperature.  If  we  bore  into  the 


HEAT-ENGINES.  285 

earth  there,  it  will  in  general  grow  warmer  as  we  go  down, 
until  a  temperature  of  —-20°  is  reached.  At  lower  depths, 
the  temperature  will  be  higher.  If  we  follow  the  isotherm 
Of  _  20°  southward,  it  will  finally  come  to  the  surface,  then 
rise  into  the  air,  and  envelop  the  equatorial  regions  of  the 
earth  at  a  point  far  above  the  isotherm  of  70°.  To  the 
southward,  the  isotherm  of  —20°  again  dips  to  the  earth, 
and  holds  a  part  of  the  antarctic  land,  like  that  of  the  arctic 
region,  in  its  cup-shaped  basin.  It  could,  however,  never 
enter  unfrozen  water  (why?),  but  would  in  arctic  seas  lie 
within  the  ice,  or  in  the  air  very  close  to  the  water. 

Frequently  in  winter  the  isotherm  of  —20°  dips  to  the  earth  in 
a  local  down-pour  of  cold  air  in  the  latitude  of  Chicago,  and  even  oc- 
casionally as  far  south  as  St.  Louis. 

In  Fig.  155,  the  isotherms  are  drawn  as  if  the  arctic  regions  were 
occupied  by  land  ;  but  of  course  they  are  not  drawn  to  proper  scale. 
Other  isotherms  between  those  of  —20°  and  70°  are  shown,  and  it  is 
left  to  the  reader  to  understand  them  without  further  explanation. 

It  will  be  seen  that  every  isothermal  surface  in  and  around  the 
earth,  including  all  artificial  sources  of  heat,  is  a  completely  closed 
surface,  and  surrounds  a  region  where  the  temperature  is  either  warmer 
or  colder  than  it  is  on  that  surface. 


APPLICATION  OF  HEAT  IN  THE  PRODUCTION  OF 
WORK. 

Heat-Engines. — Heat  is  extensively  utilized  to  save 
man  labor.  A  heat-engine  is  a  machine  in  which  heat  is 
transformed  into  mechanical  energy,  and  is  thus  enabled  to 
perform  work  by  means  of  the  expansive  force  of  steam, 
hot  air,  or  exploding  gas.  The  expansive  force  of  powder 
when  ignited  in  a  gun-barrel  imparts  motion  to  the  bullet 
— hence  a  gun  is  a  simple  heat-engine. 

The  oldest  heat-engine  known  is  described  in  the  "  Pneumatics  "  of 
Hero,  a  Greek  philosopher  who  experimented  at  Alexandria  about  150 
B.  c.  It  consisted  of  a  vessel  of  water,  A  B,  closed  securely  by  a  lid, 
and  communicating  through  the  tube  on  the  right  with  a  hollow  ball 


HEAT. 


above.  Opposite  was  a  pivot  resting  on  the  lid,  and  the  ball  was  pro- 
vided with  two  jets,  bent  at  right  angles  near  their  outer  edges,  as 
shown  in  Pig.  156.  As  soon  as  heat  was 
applied  to  the  vessel,  steam  entered  the  ball 
and  issued  violently  from  the  mouth  of  each 
jet,  causing  the  ball  to  revolve.  Hero's  was 
a  simple  rotary  engine. 

Little  attention  was  given  to  the 
development  of  the  heat-engine  from 
the  time  of  Hero  until  the  seventeenth 
century.  The  study  of  the  applica- 
tion of  steam  was  then  resumed,  and 
successive  improvements  have  been 
made  in  steam  motors  by  various  in- 
vestigators until  the  present  perfection  has  been  attained. 

The  Modern  Steam-Eiigine  utilizes  the  pressure  of 
steam  for  doing  work.  The  steam  is  generated  in  a  boiler, 
B  (see  Fig.  158),  and  is  conveyed  to  a  cylinder,  C,  through  a 
steam-chest,  S.  The  steam-chest  contains  a  valve,  V,  which 


FIG.  156.— HERO'S  STEAM- 
ENGINE. 


FIG.  157.— MODERN  STEAM-ENGINE. 


is  moved  to  and  fro  by  the  rod  A,  admitting  steam  first  at 
one  end  of  the  cylinder  and  then  at  the  other.     The  press- 


THE  MODERN   STEAM-ENGINE. 


287 


ure  of  the  steam   is   thus   applied  alternately  on  opposite 
sides  of   the  piston,  driving  it  to  and  fro.     The  power  is 
o_          transmitted  through  the  pis- 
ton-rod   R    to    the    driving- 
shaft,  as  shown  in  Fig.  157. 

The  piston-rod  terminates 
in   a   cross-head   moving  be- 
tween  guides,   thus   securing 
a  straight-line  motion.     The 
cross-head  is  connected  with 
the  crank-pin  upon  the  bal- 
anced disk  of  the  main  shaft 
by  the  connecting-rod 
E'  (see  Fig.  157).   The 
valve-rod,  A  (see  Fig. 
158),  is  driven  to  and 


fro  by  power  derived 
from  the  main  shaft,  as 
is  shown  in  Fig.  157,  where 
S  represents  the  main  shaft. 


288  HEAT. 

A  circular  disk,  e,  is  eccentrically  mounted  upon  the 
shaft  and  can  be  rigidly  connected  in  any  desired  position 
by  a  set  screw.  Surrounding  the  eccentric  is  a  collar,  with- 
in which  the  eccentric  turns  when  the  shaft  is  revolved. 


FIG.  159.— ECCENTRIC  FOR  MOVING  THE  SLIDE-VALVE. 


The  other  end,  «,  of  the  eccentric  frame  being  connected 
with  the  valve- rod,  it  is  evident  that  the  valve  will  slide  to 
and  fro  with  every  revolution  of  the  shaft. 

At  each  stroke,  the  steam  on  the  driven  side  of  the  piston  is  put 
in  communication  with  the  air  and  is  swept  out  through  the  exhaust- 
pipe  E  (Fig.  158).  As  here  shown,  the  steam  is  entering  the  head  end 
of  the  cylinder,  and  the  crank  end  is  connected  with  the  exhaust-pipe 
E.  The  student  should  make  a  drawing  showing  the  position  of  the 
valve  on  the  return-stroke,  when  these  connections  are  reversed. 

In  some  engines,  the  exhaust-pipe  E  connects  with  a  condenser 
shown  in  the  lower  part  of  Fig.  158.  The  exhaust-pipe  would  be 
connected  at  E',  leading  the  steam  into  a  chamber,  W,  surrounded 
with  water  contained  in  a  tank,  T.  Water  is  pumped  into  this  tank 
and  escapes  by  a  waste-pipe.  This  water  condenses  the  steam.  At 
the  same  time  an  air-pump  connected  with  the  pipe  P  pumps  air, 
water,  or  steam,  from  the  condenser,  delivering  the  water  to  a  tank 
called  the  "hot  well."  The  water  required  to  supply  the  boiler  is 
taken  from  the  hot  well  by  a  force-pump  or  an  injector. 

The  effectiveness  of  the  condenser  is  vastly  increased  by  admitting 
water  from  the  tank  T  into  the  condenser  through  a  short  pipe  termi- 
nating in  a  bulb,  or  "  rose,"  with  fine  holes  for  spraying  the  condens- 
ing steam.  This  supply  is  regulated  by  a  valve  controlled  at  F.  As 
the  pressure  in  the  condenser  is  considerably  below  that  of  the  at- 
mosphere, the  water  will  flow  in  if  this  valve  is  opened. 

Engines  which  exhaust  their  steam  directly  into  the  air 
are  called  Non-condensing  Engines.  The  back  pressure  on 
the  exhaust  side  of  the  piston  is  never  less  than  the  atmos- 
pheric pressure. 


THE  MODERN  STEAM-ENGINE.  289 

In  condensing  engines,  the  back  pressure  is  that  of  the 
condenser.  This  pressure  will  depend  upon  the  tempera- 
ture of  the  condensing  water  and  the  effectiveness  of  the 
air-pump.  If  the  water  entering  the  condenser  contained 
no  air,  the  pressure  would  be  determined  wholly  by  the 
temperature  of  the  water.  If  this  temperature  were  60° 
Fahr.,  the  pressure  in  the  condenser  would  be  about  half  an 
inch  of  mercury  (according  to  the  table,  page  257,  it  would 
be  O518  inch)  or  -fa  atmosphere.  The  pressure  in  the  con- 
denser is  usually  about  -fa  atmosphere. 

In  large  stationary  engines,  and  particularly  where  water  is  cheap, 
the  condenser  is  an  advantage.  For  the  same  boiler  pressure,  the  ef- 
fective pressure  on  the  piston  is  increased  by  about  -£,-  atmosphere,  as 
the  back  pressure  is  diminished  by  that  amount. 

The  Injector. — The  feed -water  from  the  hot  well  is 
forced  into  the  boiler  by  a  pump,  and  it  is  common  to  use 
an  injector  also. 

The  principle  of  the  injector  may  be  understood  from  Fig.  160. 
A  glass  tube,  A  B,  of  about  half  an  inch  diameter,  has  within  it  a  tube 
which  fits  rather  close-  ^ 

ly  and  is  sealed  in  p<>-      r "^^^^^^^-^        -  

sition     with     sealing-     = ,' — '     ^"^-- 


wax.     The  inner  tube  FlG   16o._pRINCIPIjE  OF  INJECTOR. 

is  at  one  point  drawn 

down  to  a  diameter  of  about  ^  inch.  The  outer  tube  simply  serves 
to  protect  the  inner  one  from  breaking  at  its  narrow  part.  Force 
water  through  the  tube  from  a  hydrant.  A  break  will  be  observed  in 
the  water  column  just  after  it  passes  the  narrow  part ;  it  will  appear 
like  snow-white  foam.  At  the  same  time  a  rattling  sound  will  be  heard 
like  that  made  when  a  jet  of  steam  is  discharged  under  water. 

If  the  section  of  the  tube  at  a  a  is  -^  of  the  section  at  the  wide 
part,  the  velocity  of  the  water-particles  at  the  small  section  will  be  ten 
times  as  great  as  at  the  wide  part,  since  the  same  amount  of  water 
passes  through  one  section  as  the  other  in  each  second.  The  moving 
energy  of  a  particle  at  the  narrow  part  will  therefore  be  100  times  as 
great  as  a  moment  later  when  it  has  reached  the  wider  part.  Just  at 
the  place  where  the  tube  widens,  the  water  ceases  to  fill  it  if  the 
hydrant  pressure  is  sufficient.  The  swiftly  moving  particles  in  minute 


290  HEAT. 

spherules  shoot  across  the  vacuum  formed  and  bombard  the  more 
slowly  moving  mass  in  front,  producing  the  sound  heard  and  main- 
taining the  width  of  the  gap  in  the  water  column. 

The  feed-water  injector  is  a  similar  device.  One  form  of  it  is 
shown  at  I  (Fig.  158).  Steam  from  the  boiler  passes  through  the  tube 
K  and  escapes  through  a  small  cone-shaped  nozzle  into  a  slightly 
wider  nozzle  upon  the  feed-pipe  J.  The  pipe  J  leads  back  to  the  boiler 
below  the  water-line.  The  two  nozzles  are  inclosed  by  a  pipe,  P',  which 
dips  into  the  feed- water  in  the  hot  well.  The  steam  rushes  through  the 
narrow  opening,  condensing  to  water  as  it  passes  through  the  feed- 
water,  which  must  cover  the  gap  between  the  two  pipes,  and  goes  back 
into  the  boiler,  carrying  the  feed- water  with  it. 

The  Governor  is  an  ingenious  piece  of  mechanism  de- 
signed to  make  the  engine  run  steadily  by  regulating  the 
admission  of  steam  (see  G,  Fig.  157).  It  consists  of  two 
heavy  iron  balls  which  revolve  about  a  spindle  driven  by  the 
engine,  and  which,  under  the  influence  of  the  centrifugal 
tendency,  fly  out  from  the  spindle  in  proportion  to  the  rapid- 
ity of  revolution.  In  moving  out,  they  act  in  a  certain 
manner  on  the  regulator  of  the  engine,  which  may  be  a 
throttle- valve  between  the  engine  and  the  boiler,  and  cut  off 
the  supply  of  steam.  As  they  fall  toward  the  spindle,  the 
valve  is  opened  and  steam  again  admitted. 

Air  and  Gas  Engines  include  those  machines  in  which 
the  working  element  is  air  or  some  gaseous  product  of  com- 
bustion. A  piston  may  be  driven  with  great  velocity  by  the 
elastic  force  of  heated  air,  or  by  the  expansion  of  a  mixture 
of  gas  and  air  at  the  moment  of  explosion.  Otto's  silent 
gas-engine  is  operated  on  the  latter  principle,  a  dilute  mixt- 
ure of  coal-gas  and  air  being  ignited  in  the  cylinder  under 
a  pressure  of  three  atmospheres.  A  governor  regulates  the 
admission  of  the  gas.  Gas-engines  possess  an  advantage  not 
only  in  being  easily  made  ready  for  use,  but  also  in  the  lim- 
ited amount  of  fuel  consumed. 

The  Naphtha-Engine. — The  vapor  of  deodorized  naph- 
tha has  proved  a  safe  and  easily  controlled  source  of  power 


THE  NAPHTHA  LAUNCH.          291 

in  a  motor  recently  devised.  The  naphtha  is  confined  in 
a  tank.  Gas  coming  from  this  naphtha  is  forced  through 
a  pipe  to  a  burner,  where  it  is  ignited  and  heats  a  retort  or 


FIG.  161.— LAUNCH  EQUIPPED  WITH  NAPHTHA- 
ENGINE. 

coil,  prominent  in  Fig.  160  on  top  of 
the  engine.  When  the  coil  is  suffi- 
ciently hot,  liquid  naphtha  is  forced 
into  it.  This  at  once  vaporizes  and  expands,  thus  creating 
pressure  on  the  cylinder,  as  indicated  by  a  gauge,  and  this 
pressure  is  utilized  to  move  the  machinery.  As  the  naph- 
tha-pump is  connected  by  an  eccentric  with  the  main  shaft, 
at  each  revolution  of  this  shaft  naphtha  is  automatically 
supplied  to  the  boiler.  An  injector  communicating  with 
the  retort  supplies  a  portion  of  the  vapor  regularly  as  fuel. 

The  engine  above  described  is  used  in  the  naphtha  launches  of  the 
Gas-Engine  and  Power  Company,  of  New  York.  The  machinery  occu- 
pies little  space,  and  is  manageable  by  a  child.  There  is  freedom  from 
the  dirt  inseparably  associated  with  the  use  of  coal,  and  the  expense  of 
running  the  engine  is  small. 

QUESTIONS.— Explain  isothermal  lines.  Show  how  isotherms  change  their  posi- 
tion. How  are  their  general  movements  modified  ?  If  a  thermometer  be  car- 
ried upward  from  a  point  on  the  earth's  surface,  and  then  moved  southward, 
how  may  a  temperature  of  70°  be  maintained  ?  How,  after  crossing  the  equa- 
tor ?  What  are  isothermal  surfaces  ?  Are  there  isothermal  surfaces  within 
the  earth  ?  Show  how  this  may  be.  Trace  the  isotherm  of  20°  F.  Construct  a 
diagram  illustrating  approximately  the  isotherms  of  20*  and  70°  F. 

What  are  Heat-engines  ?  Illustrate  in  the  case  of  a  gun-barrel.  Describe  the 
oldest  known  heat-engine.  The  modern  steam-engine,  reproducing  the  figure 
in  its  essential  details.  What  is  the  eccentric  ?  the  injector  ?  the  governor  ? 
State  the  difference  between  condensing  and  non-condensing  engines.  Explain 
the  principle  of  air  and  gas  engines  ;  of  the  naphtha-engine. 


292  HEAT. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

Sum  up  the  properties  of  heat  you  have  become  acquainted  with  in  the  preceding 
lessons.  When  is  a  body  hot  ?  When  cold  ?  When  do  bodies  feel  neither  hot 
nor  cold  ?  Sum  up  the  general  effects  of  heat. 

The  temperature  of  a  school-room  in  North  Dakota  was  60°  F.,  while  outside,  the 
reading  of  the  thermometer  was  52°  F.  below  the  freezing-point.  Express  the 
difference  in  degrees  Centigrade.  Express  0°  F.  on  the  Centigrade  scale. 

The  extreme  range  of  temperature  at  Werchojansk,  in  Siberia,  is  185°  F.  Express 
this  in  degrees  Centigrade  ;  in  degrees  Reaumur.  Is  this  change  in  tempera- 
ture as  great  as  the  difference  between  the  freezing  and  boiling  points  of  water? 

The  temperature  of  the  earth's  crust  rises  about  100°  F.  for  the  first  mile  of  de- 
scent toward  the  earth's  center.  How  many  feet  of  descent  will  involve  a  rise 
of  1°  C.  ?  How  many  centimetres  ?  (See  table,  p.  540.) 

Why  should  the  walls  of  a  cellar,  if  exposed  to  frost,  contain  no  stones  that  pro- 
ject into  the  soil  ?  (Expansion  of  water  in  freezing ;  principle  of  lever.) 

Instance  an  exception  to  the  rule  that  bodies  are  contracted  by  cold. 

Why  do  you  run  the  risk  of  breaking  a  tumbler  by  pouring  hot  water  into  it,  and 
why  does  a  silver  spoon  placed  in  the  tumbler  remove  the  danger  ? 

How  many  times  its  volume  does  water  expand  when  converted  into  steam  at 
100°  C.  ?  Under  a  pressure  of  one  atmosphere,  how  many  cubic  inches  of 
steam  may  be  generated  from  two  cubic  inches  of  water  ?  If  51,000  cubic  feet 
of  steam  be  condensed,  how  much  water  will  result  ? 

Suppose  six  pounds  of  quicksilver  at  100°  C.  to  be  mixed  with  two  pounds  of  iced 
water,  and  the  temperature  of  the  mixture  to  be  9°  C.  Find  the  specific  heat 
of  quicksilver. 

If  five  pounds  of  steam  at  100°  C.  are  forced  into  32  pounds  of  water  at  15°,  what 
will  be  the  resulting  temperature  ?  Ans.  99'6°. 

If  50  grammes  of  ice  at  a  temperature  of  — 10°  C.  are  put  into  400  grammes  of 
water  at  a  temperature  of  80°,  the  temperature  of  the  mixture  will  be  617°, 
what  is  the  specific  heat  of  ice  ?  Ans.  0'47.  Careful  experiment  shows  the 
specific  heat  of  ice  to  be  0'489.  . 

How  much  shorter  is  a  surveyor's  steel  chain,  100  links  in  length,  at  the  freezing- 
point  than  at  summer  heat,  or  75°  F.  ? 

Which  is  warmer  to  the  touch,  a  conductor  or  a  non-conductor  ?  On  what  prin- 
ciple is  the  shell  of  a  modern  breech-loading  shot-gun  exploded  ?  On  what 
principle  was  the  old  flint-lock  discharged  ?  Why  is  glass  so  perfect  a  protector 
of  young  plants  rooted  in  a  hot-bed  ? 

Suppose  the  reading  of  the  wet  bulb  of  a  psychrometer  to  be  25°,  and  the  temper- 
ature to  be  29°  ;  find  the  dew-point. 

How  does  the  heat  which  the  hand  receives  when  held  six  inches  from  a  lighted 
Duplex  burner  compare  with  what  it  receives  at  a  distance  of  two  feet  ? 

The  mean  distance  of  the  sun  from  the  earth  is  93,000,000  miles  ;  that  of  the  moon 
is  239,000  miles.  If  the  sun  were  as  near  as  the  moon,  about  how  many  times 
as  much  heat  should  we  receive  from  it  ? 

Venus,  at  times  the  brilliant  evening  star,  is  67,000,000  miles  from  the  sun  ;  how 
does  its  solar  heat  compare  with  ours  ? 

The  distance  from  New  York  to  Chicago  is  977  miles.  Find  the  difference  be- 
tween the  total  length  of  the  steel  rails  connecting  these  cities,  on  the  hottest 
day  in  summer  and  that  on  the  coldest  day  of  winter,  assuming  the  tempera- 
ture to  vary  from  20°  below  zero  to  90°  above  If  the  rails  are  30  feet  in  length, 
what  space  must  be  left  between  the  ends  ? 


LIGHT. 


PROPERTIES  OF  BODIES  AS  REGARDS   THE  PRO- 
DUCTION AND   TRANSMISSION  OF  LIGHT. 

Kelatioii  between  Light  and  Heat. — All  bodies,  at 
all  times  and  at  all  temperatures,  are  in  a  state  of  molecular 
agitation  whose  energy  is  Heat  (see  page  37).  Some  of 
this  energy,  their  molecules  impart,  in  the  form  of  periodic 
vibrations,  to  the  ether,  which  is  supposed  to  pervade  all 
space,  both  inside  and  outside  bodies,  and  to  exist  in  the 
most  nearly  perfect  vacuum  which  we  can  produce.  The 

NOTE.— The  following  outfit,  in  part  illustrated  above,  is  suggested  to  the 
young  experimenter :  No.  1  represents  a  combination  of  cylindrical  lenses  de- 
signed to  illustrate  the  correction  of  astigmatism  (see  page  349)  ;  2,  a  Newton's 
disk  and  rotator  ;  3,  a  double  concave  lens,  mounted  ;  4  and  5,  glass  prisms, 
mounted  ;  6,  a  pocket  microscope  ;  7,  a  plano-convex  lens  ;  8,  a  convex  mirror  ; 
9,  a  double  convex  lens  or  reading-glass  ;  10,  Prof.  Mayer's  he'liostat,  described 
on  page  299.  The  pupil  is  advised  to  supply  himself  with  a  complete  set  of  six 
demonstration  lenses,  unmounted,  a  NicoFs  prism,  a  concave  and  a  convex  mir- 
ror, a  mirror  of  black  glass,  a  three-inch  prism,  and  a  crystal  of  Iceland  spar. 
This  collection  will  be  furnished  by  any  instrument-dealer  at  a  moderate  price. 
Small  concave  and  convex  mirrors  and  burning-glasses  may  be  purchased  at 
the  toy-stores  for  a  few  cents.  The  rotator  and  heliostat  illustrated  above  are 
furnished  at  a  moderate  cost  by  Samuel  Hawkridge,  instrument-maker  to  the 
Stevens  Institute,  Hoboken,  N.  J. 


294  LIGHT. 

energy  of  ether  vibration,  however,  is  not  heat  energy ;  it  is 
another  of  the  forms  described  on  page  38,  and  is  called 
Radiant  Energy.  The  process  of  emitting  radiant  energy 
is  Radiation. 

The  ether- vibrations  pass  off  in  all  directions,  by  a  species 
of  wave-motion,  with  great  velocity.  If  these  waves  impinge 
upon  objects,  the  radiant  energy  is  transformed,  producing 
effects  determined  by  the  nature  of  the  body  upon  which 
they  fall.  On  the  skin,  they  cause  the  sensation  of  warmth  ; 
on  a  thermometer,  a  rise  of  temperature — indicating  in  each 
case  that  radiant  energy  has  been  turned  into  heat.  But 
the  most  remarkable  effect  is  that  produced  when  the  radia- 
tions strike  the  eye,  and  are  converted  in  the  mysterious 
structures  of  the  retina  into  proper  stimuli  of  the  optic 
nerve  fibers.  When  such  radiations  are  between  certain 
limits  of  wave-length,  these  fibers,  thus  stimulated,  become 
the  means  of  awakening  in  the  brain  the  sensation  which 
we  call  Light. 

The  word  Light  is  commonly  used  in  the  sense  of 
Radiant  Energy ;  it  is  thus  employed  in  what  follows. 

As  some  air- waves  do  not  excite  sound-sensations  because  they 
vibrate  too  quickly  or  too  slowly  (see  page  399),  so  there  are  ether- 
vibrations  which  do  not  affect  the  optic  nerve.  "When  vibrations  are 
properly  timed,  very  striking  mechanical  and  chemical  effects  may 
occur.  An  army  of  men  keeping  step  on  a  bridge  set  it  into  strong 
vibration,  and  may  shake  it  down.  In  like  manner,  light- waves  falling 
upon  silver  salts  used  in  photographic  plates,  cause  a  vibration  which 
shakes  asunder  the  particles  of  which  they  are  composed. 

A  Luminous  Body  is  one  which  emits  light.  When 
the  light  originates  with  the  radiating  body,  the  latter  is 
said  to  be  self-luminous.  The  sun,  whose  surface  is  com- 
posed of  exceedingly  hot  and  brilliant  clouds,  the  flame  of 
a  candle  or  a  gas-jet,  a  fire-fly,  are  self-luminous.  Other 
bodies,  like  the  moon  and  most  of  the  objects  surrounding 
us,  are  seen  by  reflected  light,  which  originates  in  some  self- 
luminous  body.  They  are  said  to  be  illuminated. 


PROPAGATION  OF   LIGHT.  295 

When  light  passes  through  space  which  is  occupied  by  matter, 
part  of  the  light  is  always  quenched  or  extinguished.  It  is  sometimes 
said  to  be  absorbed. 

Transparent  Bodies  absorb  very  little  light.  Objects 
can  be  seen  through  them  distinctly.  A  perfectly  transpar- 
ent body  would  be  invisible. 

Glass,  water,  and  air  are  transparent.  When  glass  or  ice  is  pulver- 
ized, light  is  quenched  by  repeated  reflections  from  the  internal  faces 
of  particles  which  present  themselves  at  all  possible  angles  to  the  rays. 
Such  a  mass  is  said  to  be  opaque  ;  it  intercepts  rays  of  light  and  casts 
a  shadow.  Snow  or  crushed  ice  united  into  a  continuous  mass  by 
pressure  becomes  transparent.  A  translucent  body  allows  some  light 
to  pass  through,  but  objects  can  not  be  seen  through  it. 

Opaque  Bodies  become  translucent,  and  even  trans- 
parent, when  in  thin  layers.  The  sun  may  be  seen  through 
a  thin  layer  of  silver  deposited  on  the  object-glass  of  a  tele- 
scope, although  a  less  brilliant  body  would  be  invisible. 

All  substances,  even  those  which  are  transparent,  intercept  some 
of  the  light  which  they  receive.  The  sun's  rays  lose  much  of  their 
brilliancy  by  passing  through  the  earth's  atmosphere.  As  we  ascend 
above  sea-level,  less  and  less  light  is  absorbed,  and  the  heavenly  bodies 
become  more  distinctly  visible. 

PROPAGATION  AND  VELOCITY   OF  LIGHT. 

Light  moves  in  Straight  Lines. — When  a  beam  of 
sunlight  is  reflected  into  a  darkened  room,  its  path  is  re- 
vealed by  illuminated  particles  of  dust.  This  path  is  ob- 
served to  be  straight.  We  see  each  point  of  every  object 
by  means  of  the  light  which  it  radiates.  If  light  did  not 
travel  in  a  straight  line  through  the  sights  of  a  rifle  to  the 
eye,  it  would  be  impossible  accurately  to  direct  the  ball. 

Images  by  Small  Apertures. — A  result  of  the  recti- 
linear path  of  light  is  shown  in  the  formation  of  images  by 
small  apertures.  If  a  minute  opening  be  made  in  the  side 
of  a  dark  box  or  chamber,  and  the  light  which  enters  be  re- 
ceived on  a  screen,  images  of  external  objects  will  be  seen 


296 


LIGHT. 


in  an  inverted  position — that  is,  the  objects  will  be  repre- 
sented as  upside  down.  These  images  reproduce  the  objects 
in  form  and  color. 

The  light  which  passes  through  the  opening  from  each  point  of 
the  object  falls  upon  a  definite  point  of  the  screen  and  on  no  other. 
The  image  is  thus  a  continuous  series  of  innumerable  bright  spots. 
The  screen  may  be  at  any  distance  from  the  opening.  The  size  of  the 


FIG.  163.— FORMATION  OP  IMAGE  BY  SMALL  APERTURE. 

image  will  be  observed  to  increase,  while  its  brightness  diminishes, 
as  this  distance  increases. 

Pierce  a  sheet  of  paper  with  a  pin  and  allow  sunlight  to  pass 
through  the  opening  and  fall  upon  another  sheet  of  paper.  A  round 
image  of  the  sun  will  be  seen.  If  a  second  hole  be  made,  there  will  be 
two  images,  which  will  overlap  if  the  screen  be  far  enough  away  (Fig. 
164).  Continue  to  pierce  holes  near  together.  Each  one  will  yield  a 
new  image.  As  the  paper  wears  out  and  the  holes  break  into  one  an- 
other, the  screen  shows  a  luminous  patch  of  light.  A  window-opening 
may  be  supposed  to  be  made  up  of  an  infinite  number  of  small  open- 
ings placed  side  by  side,  and  the  patch  of  sunlight  on  the  floor  to  be 
an  infinite  number  of  overlapping  images  of  the  sun.  A  single 
image  would,  therefore,  be  produced  only  by  an  extremely  small  open- 
ing. Let  the  pupil  explain  why. 


VELOCITY   OF  LIGHT. 


297 


The  brightness  of  the  image  decreases  as  the  opening  becomes 
smaller.    The  latter  may  have  any  shape,  if  small ;  but  is  incapable  of 
producing  an  image,  if  large.     Images  of  the  sun  may  often 
be  seen  on  the  floor  where  sunlight  streams  through  small 
apertures  in  the  blinds,  and  on  the  ground  where  light 
shines  through  the  foliage.    In  a  partial  eclipse  of 
the  sun,  these  images  have  been  observed  to  be 
crescent-shaped.      Why?      Such  images    can 
be  photographed  by  substituting  a  plate 
with  a  small  opening  for    the  lenses  of 
an  ordinary  camera. 


FIG.  164.— FORMATION  OF  OVERLAP- 
PING IMAGES  OF  THE  SUN. 


Velocity  of  Liglit. — Light  travels  in  space  with  a  ve- 
locity of  about  186,000  miles  a  second.  This  fact  was  first 
determined  by  Koemer  (ro'mer),  a  Danish  astronomer,  some 
two  hundred  years  ago.  He  made  observations  on  the 
nearest  of  Jupiter's  satellites,  which  revolves  round  that 
planet  as  the  moon  does  round  the  earth,  and  which  at 
regular  intervals  passes  behind  or  into  the  shadow  of  the 
planet  and  is  eclipsed — that  is,  becomes  invisible  to  an  ob' 
server  on  the  earth.  / 

(Consult  Fig.  165.) 

Roemer  noticed 
that  when  the  earth  is 
at  E,  the  interval  be- 
tween the  invisible  pe- 
riods is  42  hours,  28 
minutes,  and  36  sec- 
onds ;  but  that  as  the 
earth  moves  in  its  or- 
bit, or  pathway  round 
the  sun,  to  A  and  E',  directly  away  from  Jupiter,  this  interval  length- 
ens. By  the  time  the  earth  reaches  E',  the  eclipse  has  fallen  behind  16 
20 


FIG.  165.— ROEMER'S  METHOD  OF  DETERMINING 
THE  VELOCITY  OF  LIGHT. 


298  LIGHT. 

minutes  and  36  seconds.  As  the  revolutions  of  the  satellite  take  place 
in  exactly  the  same  number  of  hours,  the  apparent  lengthening  of  the 
interval  between  the  eclipses  can  be  explained  only  on  the  supposition 
that  light  from  the  satellite  m  occupies  time  in  its  passage  through 
space  to  the  earth,  and  that  this  time  is  lengthened  by  the  motion  of 
the  earth  away  from  the  satellite.  In  traversing  the  distance  E  E',  or 
twice  the  distance  of  the  earth  from  the  sun  (186,000,000  miles),  16 
minutes  and  36  seconds  are  consumed.  It  was  thus  an  easy  matter  for 
Roemer  to  determine  how  far  light  traveled  in  a  single  second.  How 
is  the  apparent  interval  between  successive  eclipses  affected  as  the 
earth  moves  back  again  to  E  f 

The  velocity  of  light  has  been  determined  by  other 
methods,  with  closely  agreeing  results.  While  one  is  pro- 
nouncing its  name,  light  might  travel  eight  times  the  dis- 
tance round  our  earth.  The  remoteness  of  the  fixed  stars 
from  us  may  be  inferred  from  the  fact  that  the  time  re- 
quired for  the  passage  of  light  from  those  that  are  more 

distant  is  estimated  at 
many  thousands  of 
years.  It  thus  be- 
comes possible,  through 
the  instrumentality  of 
light,  in  a  measure  to 
conceive  of  the  vast- 
ness  of  space. 

Seeing  an  Object. 

Fio.  166.— CONES  OF  LIGHT. 

— Each    point    of    an 

object  sends  rays  of  light  in  all  directions.  We  see  any 
point  by  means  of  a  cone  of  rays  whose  vertex  is  at  the 
point  and  whose  base  is  the  pupil  of  the  eye.  If  we  view 
the  object  from  a  different  position,  we  see  it  by  means  of  a 
different  cone  of  rays,  which,  however,  have  diverged  from 
the  radiant-points. 

QUESTIONS.— What  relation  can  you  discern  between  Heat  and  Light  ?  What  ob- 
vious distinction  ?  What  is  radiant  heat  ?  Do  all  heat-vibrations  affect  the 
optic  nerve  ?  Describe  the  effect  of  light  on  silver  salts.  As  regards  the  pro- 
duction of  light,  how  are  bodies  divided  ?  Distinguish  between  self-luminous 


REFLECTION  OF  LIGHT. 


299 


and  non-luminous  bodies.  How  may  non-luminous  bodies  become  visible  ? 
Whence  does  the  moon  borrow  her  light  ?  As  regards  the  transmission  of 
light,  how  are  bodies  divided  ?  What  are  transparent  bodies  ?  Translucent 
bodies  ?  Opaque  bodies  ?  How  may  opaque  bodies  become  translucent  ? 
Why  are  the  stars  more  brilliant  when  viewed  from  a  mountain-top  ? 

Describe  the  path  of  light  in  a  uniform  medium.  How  is  this  path  revealed  in  a 
dark  room  ?  Prove  that  light  travels  in  straight  lines,  from  what  is  noticeable 
in  rifle  practice  ;  from  the  lengthening  of  shadows  toward  sunset.  Explain 
what  is  formed  on  a  screen  opposite  an  aperture  in  the  shutter  of  a  dark  room. 
On  what  does  the  size  of  the  image  depend  ?  On  what  its  brightness  ?  How 
may  images  of  the  sun  be  formed  ?  What  have  you  often  noticed  on  the  ground 
when  walking  through  a  grove  on  a  sunny  day  ? 

What  is  the  velocity  of  light  ?  By  whom  was  it  determined  ?  State  the  facts 
and  reasoning  by  which  the  astronomer  arrived  at  his  conclusion.  How  long 
does  it  take  the  light  of  some  of  the  stars  to  reach  us  ?  If  the  course  of  light 
was  not  rectilinear,  how  long  would  it  be  in  flashing  around  our  globe  ?  The 
wild  pigeon  flies  with  a  velocity  of  100  miles  an  hour.  If  this  rate  of  speed 
were  maintained,  how  much  time  would  the  bird  consume  in  making  the  cir- 
cuit of  the  earth  ?  Why  can  every  person  in  a  large  audience  see  a  speaker  at 
the  same  moment  ?  Does  all  light  travel  with  the  same  velocity  ?  It  does. 


REFLECTION  OF  LIGHT.— IMAGES  BY  REFLECTION. 

Reflection  of  Light. — We  have  learned  that  light 
moves  in  straight  lines  and  is  radiated  from  luminous  bodies 
equally  in  all  directions.  When  the  radiations  or  rays  of 
light  strike  a  polished  surface,  they  are  reflected  and  take  a 
different  direction.  If  a  small  opening  be  made  in  the 

NOTE.— In  order  readily  to  obtain  a  stationary  horizontal  beam  of  light  for  ex- 
amination, Prof.  Mayer  has  devised  a  simple  form  of  the  instrument  known  as  the 
he'liostat  (sun-placer)  Fig.  167.  It  con- 
sists of  a  piece  of  board  made  of  a  size  to 
fit  the  window  selected  for  the  experi- 
ments, pierced  with  a  hole  5  inches  in 
diameter  to  admit  light  to  the  darkened 
room.  Iron  brackets  (C)  14  inches  apart 
support  a  shelf  6i  inches  wide,  on  the 
outside  edge  of  which  a  board  (D)  7 
inches  high  is  screwed,  parallel  to  the 
large  board  and  16  inches  from  it.  On 
the  shelf  is  placed  a  mirror  (O)  6  inches 

square,  standing  at  an  angle  and  facing     

the  opening  into  the  room  A  beam  of 
light  is  thrown  upon  this  mirror  from 
a  second  mirror  above  in  such  a  man- 
ner that  it  is  reflected  through  the  open- 
ing horizontally  into  the  darkened  apartment.  The  upper  mirror  (6  x  10  inches) 
is  movable,  so  that  it  can  be  adjusted  to  the  movement  of  the  sun  in  the  heavens. 


FIG.   167. 


300  LIGHT. 

shutter  at  S,  sunlight  entering  with  a  velocity  of  186,000 
miles  a  second  and  striking  a  mirror  (M),  seems  to  rebound. 
S  M  is  called  the  incident  ray,  and  M  S'  the  reflected  ray. 


FIG.  168.— ILLUSTRATING  THE  REFLECTION  OF  LIGHT. 

The  point  M  is  called  the  point  of  incidence,  and  a  line  N 
M,  perpendicular  to  the  mirror  at  that  point,  is  called  the 
normal  at  M.  The  angle  S  M  N  is  called  the  angle  of  inci- 
dence, and  the  angle  S'  M  N  the  angle  of  reflection. 

It  is  fastened  on  a  board  (N),  to  the  back  of  which  is  tightly  screwed  a  half-round 
flat  piece  of  wood  (G).  This  circular  piece  plays  in  a  slot  cut  in  a  round  length 
of  hard  wood,  being  fastened  to  the  overlapping  ends  of  the  handle  by  an  ordi- 
nary iron  bolt  and  nut.  A  hole  1}  inches  in  diameter  is  now  cut  in  the  window- 
board  and  the  handle  fitted  therein,  as  shown  in  the  cut.  Arrange  the  mirrors  so 
that  a  round  beam  of  light  will  enter  the  room,  and  turn  the  handle  of  the  instru- 
ment, as  necessary,  to  keep  the  beam  in  place.  The  size  of  the  beam  may  be  regu- 
lated by  placing  a  piece  of  cardboard  over  the  aperture,  pierced  as  desired.  In 
the  heliostat  of  the  instrument-makers,  the  sunbeam  is  kept  in  a  fixed  position 
by  the  action  of  clock-work.  (See  Mayer  &  Barnard's  "  Light,"  page  16.) 

With  Prof.  Mayer's  apparatus  (which  any  one  familiar  with  the  use  of  car- 
penter's tools  can  easily  construct),  and  the  few  lenses,  prisms,  and  mirrors, 
shown  on  page  293,  the  young  pupil  may  perform  for  himself  a  series  of  simple 
and  instructive  experiments  illustrating  the  phenomena  of  light.  A  slender  beam 
of  light  may  be  admitted  with  the  aid  of  the  heliostat,  and  leisurely  studied.  A 
hand-mirror  may  be  used  to  reflect  it,  and  it  may  be  thrown  wherever  desired  ; 
or,  if  reflected  from  a  small  piece  of  looking-glass  fastened  over  the  wrist  with 
warm  wax,  it  will  respond  amusingly,  on  the  wall  or  ceiling,  to  the  pulse-beats. 


IMAGES  BY  MIRRORS. 


301 


FIG.  169.— ANGLES  OF  INCIDENCE 
AND  REFLECTION. 


Laws  of  Reflection. — The  angles  of  incidence  and  re- 
flection are  equal. 

The  three  lines  bounding  these  two  angles 
lie  in  a  common  plane. 

A  ball  thrown  against  a  wall  will  rebound,  but  the 
angle  of  incidence  is  always  less  than  the  angle  of  re- 
flection.   A  base-ball,  suspended  like  a  pendu- 
lum and  striking  against  a  wall  to  which  it  is 
attached  (Fig.  169),  will  rebound  very  little,  and 
the  angle  r  will  be  much  larger  than  i.    If  a 
more  elastic  ball  be  taken,  the  angles 
/  will  be  more  nearly  equal.     Evident- 

ly the  ball  and  wall  must  be  perfect- 
ly elastic  in  order  to  make  the  angles 
r  and  i  equal.  If,  therefore,  the 
reflection  of  light  involves  the  re- 
bound of  elastic  particles,  as  was 
formerly  thought,  they  must  be  so 
nearly  perfectly  elastic  that  no  dif- 
ference between  the  angles  i  and  r  can  be  detected. 

Images  by  Plane  Mirrors. — Images  are  formed  by 
mirrors  in  accordance  with  the  laws  of  reflection.  Any 
radiant  point  0,  in  front  of  a  plane  mirror,  will  radiate 
light  in  all  directions.  Part  of  the  rays  will  strike  the  mir- 
ror and  will  be  reflected 
according  to  the  law  al- 
ready given,  the  angles 
i  and  r  being  equal. 

Draw  the  normal  at  any 
point  of  incidence  M'.  Draw 
also  a  normal  through  0,  pro- 
ducing it  through  the  mir- 
ror. Produce  the  reflected 

ray  through  the  mirror,  until  it  intersects  the  normal  0  M  in  I.     The 
angles  marked  (.)  are  all  equal  by  elementary  geometry,  and  0  M  =1  M. 

The  points  0  and  I  are  thus  on  opposite  sides  of  the 
mirror,  upon  a  common  normal.  They  are  also  at  equal 
distances  from  the  mirror. 


FIG.  170.— IMAGE  BY  PLANE  MIRROR. 


302 


LIGHT. 


All  reflected  rays  produced  through  the  mirror  will  in- 
tersect in  the  same  point  I.  An  eye  so  placed  that  the  re- 
flected rays  can 
enter  it,  will  see 
the  same  ap- 
pearance at  I  as 
at  0,  the  point 
from  which  the 
rays  have  really 
come.  I  is  called 

FIG.  171.— REFLECTION  FROM  WATER.  ,-,      •  »  ,  -, 

the  image  01  the 

point  0.  We  commonly  say  that  we  see  the  image  at  I,  hut 
we  are  really  looking  at  the  point  0,  by  means  of  rays  which, 
but  for  the  mirror,  would  not  have  entered  the  eye.  "We 
are  really  the  subjects  of  an  illusion  as  regards  the  position 
of  the  object  which  we  see. 

The  reflection  of  the  sun  from  water  often  appears  as  a  broad, 
illuminated  patch  of  light.  This  is  due  to  the  fact  that  ripples  or 
waves  over  a  wide  area  present  inclined  surfaces,  so  situated  that  they 


FIG.  172.— BRIDGE  OVER  THE  IOWA  RIVER,  AT  IOWA  CITY.    (VERTICAL  DISPERSION, 
DUE  TO  RIPPLES,  OBLITERATES  HORIZONTAL  LINES  IN  THE  REFLECTION.) 

reflect  light  to  the  eye.  The  rougher  the  water,  the  broader  this 
illuminated  area  will  be.  Pig.  171  illustrates  the  reflection  of  sunlight 
from  a  wave  surface.  The  reflection  of  a  bridge  from  ruffled  water 
often  shows  an  obliteration  of  all  horizontal  beams  or  arches,  because 


REVERSAL  OF  IMAGES. 


303 


of  the  dispersion  of  the  images.  The  images  of  vertical  rods  are  elon- 
gated and  indistinct  at  the  ends  only.  This  is  due  to  the  motion  of 
the  waves,  which  causes  the  reflected  light,  to  vibrate  to  and  fro,  as 
will  be  understood  from  an  inspection  of  Fig.  171. 

Reversal  of  Images. — If  you  place  before  a  mirror 
your  right  hand  grasping  a  pencil,  the  image  will  show  a 
pencil  in  the  left  hand.  This  proves  that  an  image  in  a 
mirror  is  reversed  as  regards  right  and  left,  although  it  looks 


FIG.  173.-  REVERSAL  OF  IMAGE  IN  MIKEOR. 

like  a  correct  portrait.  Every  wood-cut  and  type-face  must 
be  made  in  a  reversed  position.  When  held  before  a  mirror, 
its  image  shows  as  a  print  from  it  will  appear. 

Law  of  Least  Time. — If  a  person  were  to  run  from  a 
point  A  to  a  point  D  (see  Fig.  174),  over  uniform  ground, 
upon  which  he  could  move  with  a  constant  velocity,  the 
journey  could  be  made  in  the  least  time  if  the  path  were  the 
straight  line  from  A  to  D. 


304 


LIGHT. 


If  he  were  required  to  run  from  A  to  the  wall  B  C,  and  then  back 
to  D,  the  journey  would  be  made  in  the  least  time  if  the  point  m,  where 
he  is  reflected  from  the  wall,  were  so  chosen  that  the  two  lines  A  m 

and  m  D  would  make  equal 
angles  with  the  wall.  They 
also  make  equal  angles  with 
the  normal  at  m.  The  dis- 
tance Ami)  is  shorter  than 
the  distance  A  m"  D,  or 
the  distance  Am'"  D.  • 
In  like  manner,  light 


B 


I    M—  Ml   I  -  1 


FIG.  174.—  PATH  AND  TIME  OF  TRANSMISSION 
COMPARED. 


which   passes   from   A  to 
D,  after  reflection  from  a 

mirror  B  C,  traverses  the  path  which  makes  the  time  of  transmission 

a  minimum, 

Images  formed  "by  Two  Mirrors. — If  a  lighted  candle 
be  placed  between  two  mirrors  which  face  each  other,  the 
light  will  be  reflected  from  one  mirror  to  the  other,  each 
reflection  giving  rise  to  an  image,  which  is  an  image  of  an 
image  in  the  opposite  mirror. 

If  the  mirrors  are  exactly  parallel,  the  images  will  be  on  a  common 
normal,  and  there  will  be  an  infinite  number  of  them  at  regularly  in- 
creasing distances  from  the  mirrors.  As  some  light  is  lost  at  each 
reflection,  the  images  ^ 

decrease  in  brightness 
as  they  recede. 

In  Fig.  175,  1  is 
the  primary  image  of 
0  in  mirror  A,  2  is  an 
image  of  1  in  mirror 
B,  3  is  an  image  of  2 
in  mirror  A,  etc. 

Use  the  hand  and 
a  printed  page  as  ob- 
jects, and  notice  the  reversal  of  consecutive  images.  The  observer 
may  station  himself  behind  one  of  the  mirrors,  and  look  through  a 
pin-hole  scratched  in  its  back. 

If  the  mirrors,  instead  of  being  parallel,  are  placed  so  as  to  form 
an  angle  with  each  other,  the  images  are  limited  in  number.  This 
principle  is  applied  in  the  kaleidoscope  (ka-li1 do-scope\  a  tube  com- 


B      A 

FIG.  175. — MULTIPLICATION  OF  IMAGES  BY  PARALLEL 
MIRRORS. 


CURVED  MIRRORS.  305 

monly  containing  three  mirrors  set  at  angles  of  60°.  Pieces  of  colored 
glass,  free  to  move  at  one  end  of  the  tube,  are  seen  through  an  eye- 
hole opposite,  multiplied  by  repeated  reflections. 

Curved  Mirrors. — The  curved  mirrors  commonly  used 
as  lamp-reflectors    are    spheri- 
cal— they   are   portions   of   the 
surface  of  a  sphere. 

Spherical  mirrors  may  be 
either  concave  or  convex.  Fig. 
176  is  a  concave  mirror,  repre- 
sented by  M  0'  M'.  C  is  the 

»    ,  T  i  »       -1  •   -i        FIG.  176. — CONVERGENCE  OF  RAYS 

center  of  the  sphere  of  which  BY  CoNCAVE  MlRROR 

the  mirror  is  a  part.     C'  is  the 

center  of  the  mirror,  and  a  right  line  through  C  C'  is  called 
the  principal  axis  of  the  mirror. 

Rays  parallel  to  the  principal  axis,  striking  the  mirror  as  at  m, 
converge  to  a  point  F,  called  the  principal  focus. 

If  rays  strike  in  a  similar  manner  upon  the  convex  side,  as  in  Fig.  177, 
they  diverge,  after  reflection,  as  if  they  had  come  from  the  same  point  F. 

The  concave  mirror  converges  the  light  to  a  focus,  the 
distance  of  which  from  the  mirror  increases  as  the  mirror 

becomes  more  nearly 
plane.     The  focus  of 
a  plane  mirror  is  at 
"\~~~~ — -—...._  an   infinite    distance. 

_^'''F__— ~-  ^^  The  convex  mirror 
diverges  the  light  as 
if  it  came  from  a 
point  on  the  opposite 

FIG.  177.— DIVERGENCE  OP  RAYS  BY  CONVEX  .  . 

MIRROR.  side   of    the    mirror, 

the  distance  of  which 
also  increases  as  the  mirror  becomes  more  nearly  plane. 

Position  of  Images  formed  by  Concave  Mirrors. — 

When  light  from  a  radiant-point  at  an  infinite  distance  falls 
upon  a  concave  mirror,  the  incident  rays  will  be  parallel, 
and  will  converge,  after  reflection,  to  the  principal  focus  F. 


306 


LIGHT. 


FIG.  178.— POSITION  OP  IMAGES  BY  CONCAVE 
MIRROR. 


If  sunlight  falls  upon  a  concave  mirror,  a  small  image  of 

the  sun  will  be  formed 

^r .  O 

at  F,  and  can  be  seen 

— -- if    projected    upon    a 

C  0   bit  of  paper. 

Let  S  M  (Fig.  178)  be 
such  a  ray.  If  the  radiant- 
point  move  up  to  any  posi- 
tion 0,  the  angle  of  inci- 
dence at  M  will  be  less  than  before.  It  will  be  0  M  C  instead  of 
SMC.  The  angle  of  reflection  will  also  be  less,  since  it  is  always 
equal  to  the  angle  of  inci- 
dence. The  reflected  ray 
will  be  Mi  instead  of  M  F. 
Rays  diverging  from  0 
and  falling  upon  the  mir- 
ror will  converge  to  a  point 
i.  Thus,  while  the  object 
has  moved  from  an  infinite 
distance  to  the  point  0,  the 
image  will  move  only  from 
F  to  t. 

If  0  moves  on  up  to 
the  center  of  curvature  C, 
the  rays  from  0  will  strike  the  mirror  at  right  angles,  and  will  return 
on  their  paths,  forming  an  image  by  intersection  at  the  same  point  C. 

The  image  and  object 
coincide.  If  0  moves 
from  C  to  F,  the  image 
will  move  from  C  to  an 
infinite  distance.  The 
emergent  rays  will  be 
parallel.  The  incident 
ray  will  be  F  M  (Fig. 
179),  and  the  reflected 
ray  will  be  M  S. 

If  0  moves  from  F 
toward  the  center  of  the 

mirror,  the  rays  will  be- 
FIG.  180.— POSITION  OP  IMAGES  BY  CONVEX  MIRROR.  .  '  ,, 

gin  to  diverge  after  re- 
flection, as  M  S'  (Fig.  179).  They  will  form  no  image  on  the  concave 


FIG.  179.— POSITION  OP  IMAGES  BY  CONCAVE 
MIRROR. 


REAL  AND  VIRTUAL  IMAGES. 


307 


side  of  the  mirror,  but  will  seem  to  have  come  from  a  point  i  on  the 
opposite  side. 

As  0  moves  from  F  to  the  mirror,  the  image  will  move  from  an 
infinite  distance  on  the  convex  side  up  to  the  mirror. 

If  0  is  on  the  convex  side,  the  rays  will  always  diverge  after  re- 
flection (Fig.  180).  The  object  0  moving  from  the  mirror  to  an  infinite 
distance  on  the  convex  side,  the  image  i  moves  from  the  mirror  to  F. 

The  Object  and  Image  at  Conjugate  Points. — In 

any  position,  the  object  and  image  may  change  places.  If 
the  object  be  placed  where  the  image  is,  the  image  will  be 
formed  where  the  object  was.  This  usually  involves  a  re- 
versal of  the  direction  in  which  the  light  travels.  A  ray  of 
light  traversing  any  path,  with  any  number  of  reflections, 
will  if  reversed  retrace  that  path. 

On  account  of  this  mutual  relation  between  them,  such 
points  are  called  conjugate  (yoked  or  united  in  pairs). 

Real  and  Virtual  Images. — When  all  the  rays  of  light 
diverging  from  any  point  of  an  object  are  by  any  means 
converged  again  at  any  other  point,  we  have  a  real  image  of 
the  radiant-point.  When  the  rays  from  the  radiant-point 
are  so  changed  that  they  seem  to  have  diverged  from  some 
other  point  in  space,  a  virtual  image  is  produced. 

The  images  formed  by  plane  and  convex  mirrors  are  virtual,  as 
are  also  those  formed  by  concave  mirrors  when  the  radiant-point  is 
between  the  principal 
focus  and  the  mirror. 

Secondary  Ax- 
is of  a  Mirror. — If 

the  radiant-point  is 
not  on  the  primary 
axis  of  the  mirror,  a 
line  may  be  drawn 
through  that  point 
and  the  center  of 

~        ,  .   ,        FIG.  181.— SECONDARY  Axis  OF  CONCAVE  MIRROR. 

curvature,  C,  which 

will  intersect  the  mirror  in  some  point  M'  (see  Fig.  181). 


308  LIGHT. 

This  line  is  called  a  secondary  axis.  It  has  the  same  prop- 
erties as  a  primary  axis,  and,  like  the  primary  axis,  it  inter- 
sects the  mirror  at  right  angles,  so  that  a  ray  0  M'  will  be 
reflected  directly  back  upon  itself. 

Rays  parallel  to  this  axis  will,  after  reflection,  converge  to  a  focus 
at  a  point  midway  between  M'  and  C.  The  image  of  the  point  0  will 
be  at  a  point  i  on  the  same  secondary  axis,  and  its  position  is  deter- 
mined as  before  explained  (page  305).  0  and  i  are  on  opposite  sides 
of  the  principal  axis. 

Image  of  any  Object. — In  order  to  construct  the  image 
of  any  object,  it  is  only  necessary  to  locate  the  images  of  its 
extremities,  or  other  principal  points.  This  can  be  done  by 
drawing  secondary  axes  through  those  points. 

In  Fig.  182,  the  image  a  b  of  the  object  A  B  is  constructed.  The 
points  A  and  a  lie  on  the  same  secondary  axis.  To  determine  where, 

on  that  axis,  the  image  a 
is,  draw  any  other  ray 
from  A  to  the  mirror  and 
then  find  the  reflected  ray 
by  construction,  making 
the  angles  of  incidence 
and  reflection  equal.  The 

image  sought  will  be  some- 
FIG.  182. — MAGNIFIED  IMAGE  IN  CONCAVE  MIRROR.  , 

where  on  this  ray,  evident- 
ly at  its  intersection  with  the  secondary  axis.  In  this  case,  the  image 
a  b  will  be  larger  than  the  object. 

If  you  hold  a  concave  mirror  in  your  hand  and  look  into  it,  you  will 
see  a  magnified  virtual  image  of  your  face.  In  like  manner,  if  you 
should  construct  the  image  of  an  object  placed  directly  in  front  of  a 
convex  mirror,  you  will  understand  why  such  mirrors  give  a  dimin- 
ished image  ;  but  it  must  be  remembered  that  an  object  at  a  distance 
from  a  concave  mirror  produces  an  inverted  and  reduced  real  image. 
This  you  can  readily  prove  by  standing  near  a  window  with  a  concave 
mirror  in  your  hand,  and  casting  the  image  formed  of  outside  objects 
on  a  screen  held  just  in  front  of  the  principal  focus  of  the  mirror. 
Can  you  construct  a  diagram  to  prove  that  this  must  be  so  ? 

The  Ophthalmoscope,  an  instrument  used  by  physi- 
cians for  examining  the  interior  of  the  eye,  is  a  mirror  with 


MAGIC   MIRRORS.  309 

a  small  aperture  in  the  center.  The  mirror  reflects  light 
into  the  patient's  eye,  and  the  examiner  makes  his  observa- 
tions through  the  opening  from  behind. 

Magic  Mirrors. — The  face  of  the  ordinary  Japanese 
mirror  is  slightly,  though  not  uniformly,  convex.  This 
mirror  consists  of  a  thin  disk  of  polished  metal,  ornamented 
in  relief  on  the  back.  The  portions  of  the  mirror  in  front 
of  the  relief  work  become  plane  or  nearly  so  in  the  process 
of  manufacture,  and  hence  reflect  rays  that  are  less  diver- 
gent than  those  reflected  from  the  parts  that  remain  convex. 
If  a  bright  beam  of  light  be  reflected  from  such  a  mirror, 
which  is  partly  convex  and  partly  plane,  a  more  or  less 
well-defined  image  of  the  raised  ornaments  on  the  back 
will  appear  on  the  screen.  Mirrors  possessing  this  physical 
peculiarity  are  called  Magic  Mirrors. 

Note  the  advantage  of  Prof.  Mayer's  heliostat  in  experimenting 
with  mirrors.  It  enables  you  to  follow  satisfactorily  the  course  of  a 
single  ray. 

QUESTIONS.— Describe  the  phenomena  of  reflection.  How  may  a  horizontal  beam 
of  light  be  obtained  for  study  ?  Describe  Prof.  Mayer's  heliostat,  and  state 
its  uses.  Can  you  turn  the  ray  of  light  from  its  course  ?  State  the  laws  of 
reflection.  What  are  rays  called  that  strike  a  body  ?  Rays  that  are  thrown 
back  ?  What  can  you  say  of  the  relative  reflecting  power  of  dull  and  polished 
surfaces  ?  Why  is  a  room  with  white  walls  lighter  than  one  papered  with  a 
dark  pattern  ?  Can  you  tell  why  window-panes  sometimes  appear  fiery  red 
at  sunset  ? 

WThat  is  a  Mirror  ?  On  what  principle  do  we  see  ourselves  in  a  mirror  ?  How  far 
behind  a  plane  mirror  does  the  image  of  an  object  appear  ?  How  many  kinds 
of  mirrors  are  there  as  regards  shape  ?  What  relative  position  do  the  image 
and  object  occupy  as  regards  the  normal  ?  Show  when  they  are  equally  dis- 
tant from  the  mirror.  Show  how  we  are  deceived  in  regard  to  the  position  of 
an  object  seen  in  a  mirror.  Describe  and  explain  the  common  appearance  of 
the  reflection  of  the  sun  from  waves.  Why  is  there  an  obliteration  of  hori- 
zontal features  in  the  reflection  of  a  bridge  from  ruffled  water  ?  Explain  the 
reversal  of  images  in  mirrors.  State  the  law  of  least  time,  and  apply  it  to 
light.  Describe  the  formation  of  images  by  two  parallel  mirrors  ;  by  mirrors 
placed  at  an  angle.  What  is  the  kaleidoscope  ? 

What  are  curved  mirrors  ?  Define  the  principal  axis  and  focus.  On  what  does 
the  distance  of  the  focus  depend  ?  How  far  from  a  plane  mirror  is  its  focus  ? 
Describe  the  reflection  from  a  concave  mirror.  Discuss  the  relation  between 
the  positions  of  the  object  and  the  image  when  the  former  is  beyond,  at,  and 
within  the  center  of  curvature.  Where  must  the  object  be  to  have  the  rays  di- 


310 


LIGHT. 


verge  after  reflection  ?  What  are  conjugate  points  ?  Distinguish  between  real 
and  virtual  images.  What  is  the  secondary  axis  of  a  mirror  ?  Describe  images 
of  objects  placed  directly  in  front  of  concave  mirrors  ;  of  convex  mirrors  ;  at 
a  distance  from  concave  mirrors.  What  are  magic  mirrors  ? 


REFRACTION  OF  LIGHT. 

Refraction  illustrated. — Construct  a  rectangular  box 
having  one  side  of  glass  fastened  by  means  of  wooden  strips 
laid  in  white  lead.  Throw  a  slender  beam  of  light  S  (see 
Fig.  183),  directed  into  the  room  by  means  of  the  heliostat, 
over  the  edge  of  the  box  and  along  the  glass  side.  Note  the 
point  A  where  it  falls  upon  the  bottom.  Fill  the  box  with 
water,  and  cloud  the  water  slightly  with  a  few  drops  of  an 
alcoholic  solution  of  mastic.  The  beam  of  light  will  now 
bend  at  the  water  surface,  and  will  proceed  to  a  point  B. 


FIG.  183.— REFRACTION  OP  A  BEAM 
OF  LIGHT  IN  WATER. 


FIG.  184. — ILLUSTRATING  THE 
LAW  OF  REFRACTION. 


The  path  of  the  beam  within  the  water  will  be  a  straight 
line,  but  it  is  bent  downward,  or  refracted,  from  the  water 
surface. 

Law  of  Refraction. — To  explain  the  law  of  refraction, 
draw  a  circle  having  a  radius  of  one  unit,  say  an  inch,  foot, 
or  decimetre,  and  having  its  center  in  the  water  surface  at 
the  point  of  incidence  K,  as  in  Fig.  184.  The  incident  ray 
may  be  represented  by  a  K,  and  a  K  5  is  the  angle  of  inci- 
dence. Then  the  line  a  1)  is  called  the  sine  of  the  angle  of 
incidence.  This  is  abbreviated  sin  i. 

In  the  water,  the  ray  takes  the  direction  K  d.     This  line 


LAW  OF  REFRACTION.  311 

represents  the  refracted  ray ;  C  K  d  is  the  angle  of  refrac- 
tion, and  d  w  is  the  sine  of  the  angle  of  refraction,  which  is 
abbreviated  sin  r. 

It  is  found  by  careful  measurements  that  when  i  changes,  r  always 
changes  in  such  a  way  that  sin  i  is  always  £  of  sin  r  when  light  passes 
from  air  into  water.  If  m  K  is  the  incident  ray,  then  K  o  will  be  the 

a  b      mn      4       sin  i 
refracted  ray,  where  j^  =  —  =  g-  =  -^  • 

This  constant  ratio  between  the  sines  of  the  angles  of  incidence 
and  refraction  is  called  the  Index  of  Refraction. 

If  the  ray  enters  the  water  along  the  line  b  K,  it  will  proceed  in  the 
same  straight  line. 

If  the  ray  enters  sensibly  parallel  to  the  surface,  as  in  the  case  of 
v  K,  the  angle  of  incidence  is  90°,  and  the  sine  of  i  =  1,  or  v  K.  The 
refracted  ray  will  pass  along  a  line  K  u,  so  located  that  u  z,  or  the 
sine  of  r  =  f  of  K  v,  which  is  the  sine  of  the  angle  b  K  v. 

Strictly,  the  light  can  not  enter  parallel  to  the  surface,  but  it  may 
be  directed  into  a  globe  half  full  of  water.  If  the  light  enters  at  u,  and 
is  incident  at  K,  it  will  pass  out  along  the  surface  in  the  direction  K  v. 
Similarly,  the  light  may  be  sent  through  the  water  along  the  lines  o  K 
or  d  K,  when  it  will  pass  into  the  air  along  the  lines  K  m  and  K  a. 

Values  of  the  Index  of  Refraction. — The  bending  of 
the  ray  at  the  bounding  surface  between  two  media  is  dif- 
ferent for  different  media. 

When  light  passes  from  air  to  water,  the  index  of  refraction  is  f ; 
from  air  to  glass,  it  is  f ;  and  from  water  to  glass,  it  is  f . 

Phenomena  of  Refraction. — A  stick  partly  immersed 
in  water  appears  bent,  unless  it  stands  vertically,  when  it 
appears  shortened. 

The  rod  A  D  B  (Fig.  185)  is  bent  into  the  form  A  D  B'  when  viewed 
from  e.  The  plumb-bob  w  will  seem  to  be  at  w',  which  is  directly 
above  w.  The  plumb-line  appears  straight  throughout,  but  the  part 
below  the  water  appears  shortened. 

The  appearance  of  the  rod  may  be  found  as  follows :  From  e  draw 
e  o  or  e  o',  producing  the  lines  indefinitely  below  the  surface  o'  o  D. 
With  o  and  o'  as  centers,  draw  circles,  each  having  a  unit  radius.  Then 
the  lines  s  s  are  the  sines  of  the  angles  of  incidence,  and  the  refracted 
rays  o'  s'  and  o  s'  must  be  so  drawn  that  s'  s'  is  $  of  s  s. 


312 


LIGHT. 


Light  radiated  from  B  through  o'  will  reach  the  eye  at  e.  The 
light  will  seem  to  have  come  from  B'.  The  point  B  of  the  stick  will 

seem  to  be  at  B', 
which  is  directly 
above  B. 

The  rays  from 
an  object  below 
the  water  are  not 
brought  to  a  sharp 
focus,  so  that  such 
objects  seem  indis- 
tinct, particularly 
for  large  angles  of 

incidence.  It  is  on  account  of  refraction  that  one  must  aim  below  the 
apparent  position  of  fish  in  shooting  or  spearing  them.  Here,  as  in 
reflection  of  light,  the  eye  always  refers  the  direction  of  a  body  along 
the  direction  which  the  light  from  it  has  on  entering  the  eye. 

Apparent  Depth  of  Water. — If  one  stand  in  a  pool  of 
clear  water,  the  depth  of  which  is  everywhere  the  same,  the 
bottom  will  appear  dished.  The  water  will  seem  deepest 
just  below  the  eye.  A  few  feet  distant,  water  four  or  five 


FIG.  185.— PHENOMENA  OF  REFRACTION. 


FIG.  186.— SHOWING  THE  APPARENT  SHOALING  OF  UNIFORMLY  DEEP  WATER. 

feet  deep  may  seem  not  over  a  foot  in  depth.  If,  however, 
the  bottom  seems  flat,  the  water  would  grow  deeper  as  one 
went  outward  from  the  eye.  Many  persons  are  drowned  by 
reason  of  these  deceptive  appearances. 

The  phenomena  just  described  are  noticeable  in  a  tank  12  or  14 
inches  long  and  8  to  10  inches  deep,  if  it  be  filled  with  clear  water,  and 


PHENOMENA   OF   REFRACTION.  313 

the  eye  be  placed  near  the  water  surface.  Let  a  a  (Fig.  186)  be  the 
water  surface,  and  b  b  the  bottom,  e  being  the  position  of  the  eye. 
Then  will  b'  b'  be  the  appearance  of  the  bottom. 

Draw  lines  from  the  eye  to  any  points  in  the  surface.  At  these 
points  erect  normals,  draw  circles  of  unit  radius  around  them.  The 
position  of  the  ray  in  the  water  can  then  be  found  as  before  described. 
Produce  this  ray  to  the  bottom  b  b.  The  point  thus  determined  will 
seem  raised  vertically  to  the  prolongation  of  the  ray  passing  through  e. 


FIG.  187.— REFRACTION  OF  SUN'S  RAYS 
BY  THE  EARTH'S  ATMOSPHERE. 

An  inspection  of  Fig.  187  will  make  it  clear  that  we  see  the 
sun  both  before  it  rises  and  after  it  sets.  Suppose  the  observer  to 
be  stationed  at  A.  Rays  from  the  sun,  like  S  D,  would  not  reach 
A  at  all,  because  the  round  earth  is  in  the  way;  but  rays  like 
S  C,  passing  through  air  of  increasing  degrees  of  density,  are  re- 
peatedly bent  toward  the  normal,  until  they  reach  the  earth's  sur- 
face at  A. 

If  the  refractive  power  of  air  be  subjected  to  constant  modifica- 
tion, as  by  the  warm  currents  rising  from  a  hot  stove,  objects  viewed 
through  it  will  appear  to  have  a  wavy  or  tremulous  motion. 

Total  Reflection. — Light  striking  the  water  at  any 
angle  between  0°  and  90°,  will  enter  and  suffer  refraction, 
as  explained.  In  Fig.  188,  the  paths  of  rays  1  m  1,  2m  2, 
3  m  3,  and  4  m  4,  are  shown.  When  the  angle  in  the  air  is 
90°,  or  z  m  S',  the  sine  of  the  angle  of  incidence  is  the 
radius,  and  v  w,  which  is  }  of  the  radius,  will  be  the  sine  of 
r,  or  v  m  n.  If  the  light  were  to  be  reversed  in  direction, 
each  ray  would  retrace  its  entire  path.  If  the  incident  ray 
were  to  sweep  through  the  angle  n  m  v,  being  always  inci- 
21 


314 


LIGHT. 


dent  at  m,  the  ray  emerging  into  the  air  would  sweep 

through  the  angle  z  m  S'. 

If  the  ray  were  incident  at  m,  but  should  lie  within  the 

angle  v  m  S,  it  could  not  pass  through  the  surface  into  the 

air,  but  would  be  wholly  reflected  into  the  water,  making 

the  angle  of  incidence  equal 
to  the  angle  of  reflection. 
Under  these  circumstances,  a 
water-air  surface  is  a  perfect 
reflector  of  light. 

The  angle  v  m  n  is  called  the 
critical  angle.  If  the  incident 
angle  in  water  is  greater  than  the 
critical  angle,  total  reflection  takes 
place. 

The  phenomena  of  total  reflection  may  be  shown  by 
means  of  a  glass  cube,  such  as  is  commonly  used  as  a  paper- 
weight (see  Fig.  189). 


FIG.  188.— ILLUSTRATING  THE  CRITICAL 
ANGLE. 


FIG.  189.— TOTAL  REFLECTION  IN  THE  CASE  OF  GLASS  PAPER-WEIGHT. 

Set  the  cube  down  on  a  band  of  ruled  lines  of  exactly  the  same 
width  as  itself.    The  lines  below  the  cube  are  invisible  through  the 


TOTAL  REFLECTION. 


315 


side  faces.  The  bottom  presents  a  silvery  appearance,  like  a  mirror, 
and  seems  to  be  much  narrower  than  the  band  of  lines.  The  lead 
pencil  shown  in  the  figure  is  also  invisible  through  the  top  face,  by 
reason  of  total  reflection  from  that  face ;  but  it  is  seen  reflected  from 
the  bottom  face. 

In  the  top  face,  two  sets  of  ruled  lines  are  visible.  The  lower  lines 
are  seen  directly  through  the  bottom  of  the  cube,  their  apparent  posi- 
tion being  changed  by  refraction.  The  upper  lines  are  also  the  lines 
below  the  -cube,  seen  by  total  reflection  from  the  back  face.  These 
two  sets  of  lines  are  separated  by  the  beveled  edge  of  the  cube. 

Allow  a  film  of  water  to  creep  under  the  cube.  The  lines  below 
the  cube  can  then  be 
seen  through  the  sides, 
if  the  eye  be  somewhat 
raised ;  but  on  depress- 
ing the  eye,  the  lines 
disappear  and  the  sil- 
very appearance  of  to- 
tal reflection  is  ob- 
served. The  critical 
angle  of  glass  in  con- 
tact with  water  differs 
from  that  of  glass  in 
contact  with  air. 

The  cube  may  be  placed  on  edge  and  a  beam  of  light  (from  a  lens 
of  long  focus,  or  directed  by  the  heliostat)  sent  into  one  face  so  as  to 
strike  an  adjacent  face  from  the  inside.  Total  reflection  of  the  beam 
will  be  seen,  its  track  being  revealed  by  a  greenish  color  (see  Fig.  190). 

Light  under  Water. — Light  radiating  from  a  point  0 
(see  Fig.  191)  below  the  surface  of  water,  as  in  the  case  of  a 
submerged  electric  globe,  will  pass  out  into  the  air,  follow- 
ing the  laws  of  refraction.  All  rays  from  0,  making  an 
angle  with  the  normal  equal  to  the  critical  angle,  will  pass 
out  in  the  surface  of  the  water.  These  rays  are  marked 
0  C,  and  constitute  a  cone  whose  vertex  is  at  0.  Rays 
striking  the  water  farther  out,  and  making  an  angle  of 
incidence  greater  than  the  critical  angle,  would  be  totally 
reflected. 

An  eye  placed  at  0,  would  see  within  the  cone  COG,  all  objects 
above  the  water  surface.  The  sun  just  rising  would  be  seen  by  means 


FIG.  190.— TOTAL  REFLECTION  BY  GLASS  CUBE. 


316 


LIGHT. 


of  the  ray  S  C,  which  would  seem  to  have  come  from  C'  C.  The  whole 
water  surface  outside  of  the  points  C  would  appear  lifted  to  form  a 
cone  C'  C  C  C".  A  boat  at  a  would  seem  to  be  at  a',  a  bird  at  b  at  &', 
while  a  fish  at  /  would  be  seen  at  /',  by  total  reflection. 

These  appearances  can  be  experienced  by  sinking  quietly  below 
smooth  clear  water,  and  looking  out  through  the  surface.    If  one  is 


FIG.  191.— PHENOMENA  OF  REFRACTION  AND  REFLECTION  FROM  A  POINT  OF  VIEW 
BENEATH  THE  WATER. 

provided  with  a  rather  large  rubber  tube  through  which  to  breathe, 
they  may  be  studied  more  at  leisure. 

The  shooting-fish  of  Java  is  said  to  project  drops  of  water  from 
its  prolonged  snout  so  as  to  bring  down  insects  flying  near  the  sur- 
face. The  fish  must  then  be  able  to  allow  for  the  difference  between 
the  real  and  the  apparent  position  of  its  prey. 

Look  at  the  diagram  and  state  where  an  artificial  fly  on  the  sur- 
face at  x  would  appear  to  a  fish  at  /;  to  a  fish  at  O.  Could  an  angler 
on  the  bank  occupy  any  position  where  he  would  be  out  of  sight  of  a 
fish  in  mid  stream  f 

Value  of  the  Critical  Angle. — The  critical  angle  is 
the  angle  which  the  ray  makes  with  the  normal  in  any 
more  refracting  medium,  when  the  corresponding  angle  in 
the  less  refracting  medium  becomes  90°. 

As  in  all  cases  —. —  =  index  of  refraction,  if  i  represents  the  angle 
sin  r 

in  the  more  refracting  medium,  then  for  water-air — 

sin  i  sin  c  _  sin  c  _  3 

sin  r  ~  sin  90  ~~     1     ~~  4 


INDEX  OF  REFRACTION. 


317 


That  is,  when  r  =  90°,  i  becomes  c  or  the  critical  angle.  This  angle  is 
one  whose  sine  is  f  the  radius.  Similarly  for  glass-air,  the  sine  of  the 
critical  angle  is  f ,  and  for  glass-water  the  sine  c  is  f .  By  construction 
and  measurement  by  means  of  a  protractor,  these  angles  can  be  found 
approximately.  They  can  also  be  obtained  by  consulting  a  table  of 
natural  sines : 


Substances. 

Index  of  refraction. 

sin  c. 

c  —  critical  angle. 

water 
air 

1 

4 

48°    35' 

glass 

1 

41°    48' 

air 

8 

glass 
water 

1 

* 

62°    44' 

The  index  of  refraction  from  water  to  air  is  5,  and  from  air  to 
water  it  is  $.  The  substance  containing  the  lesser  angle  (water)  is  said 
to  be  more  refracting  than  the  substance  containing  the  greater  angle. 

The  diamond  is  a  highly  refractive  stone ;  hence  its  luster.    Cer- 
tain rays  falling  on  the  internal  surfaces  of  the  facets  are,  also,  totally 
reflected.    The  diamond's  index  of  refraction  being  about  ty,  while 
that  of  glass  is  only  f ,  we  are  furnished  with 
a  certain  test  by  which  to  detect  imitation  A 

stones. 

Applications  of  Total  Reflec- 
tion. —  The  glass  prism  of  90°  is 
frequently  used  as  a  reflector.  It  is 
more  effective  than  an  ordinary  mir- 
ror, since  all  the  light  is  reflected. 

Light  striking  the  face  A  C  at 
right  angles  passes  on  without  devia-   'Fia-  iss.— TOTALLY  REPLKCT- 
tion  to  the  diagonal  face  A  B.     The 

angle  of  incidence  there  is  45°,  which  is  greater  than  the 
critical  angle  41°  48'.  No  light,  therefore,  can  pass  through 
the  face  A  B.  It  is  all  reflected. 

The  Camera  Lucida. — The  principle  of  total  reflec- 
tion is  utilized  in  the  Camera  Lu'cida,  an  instrument  de- 
signed to  facilitate  the  drawing  of  distant  objects.  Rays 
strike  the  face  c  d  of  a  totally  reflecting  prism,  inclined  at 


318  LIGHT. 

an  angle  of  22|°.  (See  Fig.  193.)  They  are  totally  reflected 
to  the  surface  d  «,  and  thence  to  the  eye  pp.  As  the  paper 
and  pencil  to  be  used  in  the  sketch 
are  not  visible  through  the  prism, 
the  eye  must  be  so  placed  that  a 
part  of  the  pupil  projects  beyond 
the  prism.  Half  of  the  pupil  thus 
receives  the  reflected  rays,  and  the 
reflected  image  is  seen  projected  on 
the  paper  beneath.  There  is  a  mov- 

FIG.  193.— SECTION  OF  PRISM.          ,        .  .  ,        ,     ,     .        , 

able  piece  01  brass  with  a  hole  in  the. 
center,  which  serves  as  an  eye-piece. 

The  camera  lucida  is  useful,  not  only  for  drawing  objects,  but 
also  for  copying.  The  copy  may  be  reduced  to  any  size  by  regulating 
the  distance  of  the  original  from  the  prism.  You  can  construct  a 
simple  camera  lucida  by  fixing  on  a  stand  a  piece  of  plane  glass  at  an 
angle  of  45°  to  the  horizon.  An  image  of  surrounding  objects  will 
be  seen  through  the  glass  on  a  sheet  of  paper  laid  on  the  table.  The 
glass  both  reflects  the  image  and  permits  the  writing  materials  to  be 
seen  through  it,  so  that  an  outline  may  be  readily  traced.  Why  is  the 
image  in  this  case  inverted  ? 

Prisms  like  the  above  are  sometimes  fixed  at  the  eye-pieces  of 
telescopes.  They  reflect  images  of  objects  in  the  field,  so  that  draw- 
ings may  be  made. 

Velocity  of  Light  in  the  two  Media. — The  velocity 
of  light  is  greater  in  air  than  in  water ;  and,  in  general,  it  is 
greater  in  the  less  refracting  than  in  the  more  refracting 
medium. 

The  ratio  of  the  two  velocities  is  also  found  to  be  equal  to  the  in- 
dex of  refraction,  or 

sin  i       v 

—. —  =  —  =  index  of  refraction. 

Bin  r      v 

The  angle  i  is  in  the  same  medium  where  the  velocity  is  v. 

Law  of  Least  Time. — If  a  man  were  required  to  travel 
over  uniform  ground,  from  a  point  B  to  a  point  A  (see  Fig. 
194),  in  the  least  possible  time,  his  path  should  be  a  straight 


LAW  OF  LEAST  TIME. 


319 


FIG.  194.— ILLUSTRATING  THE  DIFFERENCE  OF  VELOCITY 
IN  DIFFERENT  MEDIA,  AND  THE  LAW  OF  LEAST  TIME. 


line  joining  the  two  points.  If,  however,  A  is  in  a  meadow, 
where  he  can  run  with  a  velocity  of  8  miles  an  hour,  while 
B  is  on  plowed  ground,  where  his  speed  can  not  exceed  6 
miles,  the  boundary  between  the  two  surfaces  being  li  m'  m 
h'9  then  his  path  must  be  differently  chosen. 

By  selecting  some  path  AmB,  the  total  distance  traveled  is 
greater  than  A  m'  B,  but  a  larger  fraction  of  it  is  over  the  smooth 
ground,  where  the 
velocity  is  greater. 
By  choosing  m  to  the 
right  of  m',  an  ad- 
vantage in  time  is 
gained,  notwithstand- 
ing the  greater  dis- 
tance. But  if  m  is 
chosen  too  far  to  the 
right,  as  at  h',  the  in- 
crease in  the  total  distance  will  more  than  compensate  for  the  ad- 
vantage of  traveling  the  greater  distance  over  good  ground.  The  point 
m  should  be  so  chosen  that  the  runner  is  refracted  at  the  boundary,  as 
light  is  refracted  in  passing  from  one  medium  to  another. 

If  we  consider  A  m  N  and  B  m  N'  the  angles  of  incidence  and  re- 
fraction, then 

sin  i  v 8  4 

sin  r       v'      6       3 

Mr.  Haughton  observed,  on  the  beach  near  Swansea,  some  oyster- 
women  who  furnished  an  illustration  of  this  law.  In  a  course  be- 
tween points  situated  like  A  and  B,  the  hard  walking  was  a  strip  of 
rough,  slippery  shingle  between  the  water  and  a  smooth  common. 
They  were  all  refracted  at  the  boundary-line,  unconsciously  choosing 
paths  which  reduced  their  labor  to  a  minimum.  The  path  is  the  same, 
whether  the  journey  be  from  A  to  B  or  from  B  to  A. 

PROBLEM.— If  A  h  =  2  miles,  h'  B  =  6  miles,  and  h'h  =  2Q  miles, 
find  the  distance  h'  m  for  minimum  time.  Find  the  times  for  the  four 
paths  A  h  B,  A  m'  B,  A  m  B,  A  h'  B. 

QUESTIONS. — When  light  strikes  a  transparent  body,  is  it  all  reflected  ?  In- 
stance a  familiar  example  which  proves  that  rays  are  bent  on  passing  from 
one  medium  to  another.  Explain  what  is  meant  by  the  index  of  refraction. 
State  the  index  of  refraction  for  air-water  ;  for  air-glass ;  for  water-glass. 
Describe  the  appearance  of  a  stick  partly  immersed  in  water.  Show  by  dia- 
gram how  points  on  the  stick  must  appear  to  change  their  real  positions.  Why 


320  LIGHT. 

do  fish  appear  nearer  the  surface  than  they  really  are,  and  where  must  one  aim 
in  shooting  at  fish  with  a  rifle-ball  ? 

Describe  the  appearance  of  water  to  one  look,  ng  outward  from  the  shore.  How 
much  deeper  is  water  immediately  under  a  bather  than  it  appears  to  be  ?  About 
one  third.  Is  it  true  that  we  see  the  sun  before  it  actually  rises  ?  Why  is  this  f 
Perhaps  you  can  further  explain  why  objects  on  either  side  of  a  hot  stove-pipe 
seem  to  have  a  tremulous  motion  ;  why  stars  twinkle.  What  causes  a  diamond 
to  sparkle  V  On  what  principle  may  imitation  stones  be  detected  ? 

Explain  the  phenomena  of  Total  Reflection.  Illustrate  with  a  glass  cube.  What 
is  the  critical  angle  ?  Describe  the  appearances  from  a  view-point  beneath  the 
water.  Give  an  account  of  the  shooting-fish.  Is  the  velocity  of  light  different 
in  different  media  ?  State  an  interesting  analogy  between  the  refraction  of 
light  and  the  refraction  of  a  runner  in  passing  from  smooth  to  rough  ground. 


PRISMS  AND  LENSES. 

-» 

An  Optical  Prism  is  a  refracting  mass,  bounded  by 
planes  inclined  at  any  angle.  Prisms  have  two  effects  upon 
light  passing  through  them : 

I.  The  light  is  refracted,  or  bent  out  of  its  course. 

II.  The  light  is  dispersed  into  a  spectrum  of  colors.    This 
second  effect  will  be  discussed  under  the  head  of  Color. 

Let  a  b  c  be  a  section  of  a  glass  prism  at  right  angles  to  the  edges. 
A  ray  of  light  from  o,  entering  the  prism  at  d,  is  bent  toward  the  nor- 
mal. Passing  on  to  e,  it  is  bent  away 
from  the  normal  in  again  entering 
the  air.  Both  of  these  effects  deviate 
the  ray  in  the  same  direction.  The 
object  o  appears  to  be  at  i,  in  the 

line  of  direction  which  the  ray  has  on 
Fia.  195.— REFRACTION  BY  MEANS  .  .       ,.  .   •' 

OF  A  PRISM.  reaching  the  eye.    The  original  direc- 

tion of  the  ray  was  o  h,  and  the  final 

direction  is  i  h.    The  ray  has  therefore  been  deviated  through  an  angle 
o  h  i,  which  is  called  the  angle  of  deviation. 

A  liquid  or  gas  can,  for  the  purpose  of  experiment,  be 
confined  in  a  hollow  prism  made  of  glass  plates  cemented  to 
a  triangular  frame  or  box  of  metal  or  glass.  Glass  bottles 
of  this  form  are  in  common  use. 

When  the  sides  of  a  glass  prism  are  parallel,  it  becomes 
a  plate  of  glass.  At  the  second  face,  the  ray  is  restored  to 
its  original  direction  and  proceeds  in  a  parallel  path. 


LENSES. 


321 


Loss  of  Light  by  Multiple  Reflection. — When  a  ray 
of  light  falls  upon  a  plate  of  glass,  part  of  the  light  is  re- 
flected, and  part  enters  the  glass  and  is  incident  upon  the 
second  face.  At  the  second  point  of  incidence,  the  light  is 
again  divided,  part  passing  through  the  surface  into  the  air, 
in  a  path  parallel  to  the  ray's 
original  direction,  the  other 
part  being  internally  reflected. 
This  latter  ray  strikes  the  first 
face,  where  part  passes  out  into 
the  air,  and  another  part  is 
again  internally  reflected. 

Fig.  196  shows  the  first  reflected 
ray,  two  emergent   rays    from    the 

first  face,  and  three  emergent  rays,  1',  2',  and  3',  from  the  second  face. 
The  greater  portion  of  the  light  is  contained  in  the  first  transmitted 
ray. 

Lenses  are  masses  of  glass,  bounded  usually  by  spheri- 
cal surfaces  (see  illustration,  page  293).  Various  forms  of 
lenses  in  use  are  shown  in  Fig.  197.  The  shaded  part  of  1 


FIG.  196.— Loss  OP  LIGHT  BY  RE- 
PEATED REFLECTION.  • 


FIG.  197.— FORMS  OP  LENSES  BY  INTERSECTION  OP  SPHERES. 

represents  a  double  convex  lens,  which  may  be  described  as 
the  space  common  to  two  intersecting  spheres. 

If  the  center  c'  of  the  left  hand  sphere  be  supposed  to  move  to  the 
left  an  infinite  distance,  the  size  of  the  sphere  would  be  so  increased 
that  the  part  which  intersects  the  second  sphere  would  practically  be- 
come a  plane.  A  lens  formed  by  such  an  intersection  is  a,  plano-convex 
lens,  and  is  shown  in  2. 

If  the  center  c'  be  moved  to  the  right,  the  surfaces  will  bound  a 
space  concave  on  one  side  and  convex  on  the  other,  as  in  3.  A  lens 


322 


LIGHT. 


thus  made  is  called  a  meniscus.    These  three  lenses  are  thicker  at  the 
middle  than  at  the  edges. 

If  the  two  spheres  do  not  quite  intersect,  the  space  between  their 
surfaces  will  have  the  form  of  a  double  concave  lens.  Such  a  lens 
would  be  bounded  by  the  two  spherical  surfaces,  and  a  cylinder,  whose 
axis  passes  through  the  two  centers,  as  is  shown  in  4. 


FIG.  198.— FORMS  OF  LENSES  BY  INTERSECTION  OP  SPHERES. 

Moving  the  center  c'  to  an  infinite  distance  to  the  left,  we  form 
the  plano-concave  lens  shown  in  5 ;  and,  finally,  if  the  center  c'  is  on 
the  right  of  c,  we  have  the  concavo-convex  lens  shown  in  6.  The  last 
three  lenses  are  thinner  at  the  center  than  at  the  edges. 

Definitions  regarding  Lenses. — The  center  of  curva- 
ture of  any  face  of  a  lens  is  the  center  of  the  sphere  of 
which  it  is  a  part. 

A  line  drawn  from  the  center  of  curvature  of  any  face 
to  any  point  of  that  face  is  called  the  normal  at  that  point. 

The  principal  axis  of  a  lens  is  the  line  passing  through 
the  centers  of  its  two  bounding  spheres.  If  the  radii  of 
the  two  spheres  are  equal,  the  point  on  the  principal  axis, 
midway  between  the  two  faces,  is  called  the  optical  center. 

Any  straight  line  through  the  optical  center  is  called  a 
secondary  axis. 

Lenses  1,  2,  and  3,  of  Fig.  197,  have  the  same  effect  upon  light  as 
two  prisms  with  their  bases  together.  They  cause  parallel  rays  to  con- 
verge toward  the  axis.  They  increase  the  convergence  of  converging 
rays,  or  diminish  the  divergence  of  diverging  rays.  Lenses  4,  5,  and  6 
will  diverge  rays  from  the  axis. 

Principal  Focus  of  Converging  Lenses. — The  double 
convex  lens  will  serve  as  a  type  of  converging  lenses.  The 
principal  focus  is  the  point  to  which  parallel  rays  are  con- 


FOCI  OF  LENSES. 


323 


verged,  after  passing  through  the  lens.  The  principal  focus 
of  any  lens  can  be  determined  by  a  mathematical  calcu- 
lation, when 
the  radii  of 
its  bounding 
faces  and  the 
thickness  of 
the  lens  are 


FIG.  199.— PRINCIPAL  Focus  OF  CONVEX  LENS. 


given. 

The  distance, 
F  A,  from  the 
principal  focus 

to  the  lens  is  called  the  focal  length.  It  shortens  as  the  convexity  of 
the  lens,  or  the  refracting  power  of  the  material  of  which  the  lens  is 
made,  is  increased. 

If  a  common  glass  lens  be  immersed  in  water,  the  principal  focus 
will  be  about  four  times  as  far  from  the  lens  as  it  is  in  air. 

Principal  Focus  of  a  Diverging  Lens. — When  rays 
parallel  to  the 
principal  axis 
fall  upon  a 
double  concave 
lens,  they  also 
undergo  two  re- 
fractions. But 
they  issue  from 
the  lens  in  a  di- 
vergent beam, 

which  seems  to  have  come  from  a  point  F.  This  point  is 
the  principal  focus  of  the  lens. 

Real  and  Virtual  Foci. — The  principal  focus  of  a 
double  convex  lens  is  a  real  focus.  Parallel  rays,  after  pass- 
ing through  the  lens,  are  actually  converged  there.  The 
principal  focus  of  a  double  concave  lens  is  a  virtual  focus. 
Parallel  rays,  after  passing  through  the  lens,  seem  to  have 
diverged  from  that  point. 


FIG.  200. — PRINCIPAL  Focus  OP  CONCAVE  LENS. 


324: 


LIGHT. 


If  a  double  convex  lens,  as  an  ordinary  pocket  glass,  be 
held  in  the  sunlight,  the  image  of  the  sun  is  formed  in  mid- 
air. It  may  be  rendered  visible  by  smoke  or  dust  in  the  air, 
or  it  may  be  projected  on  paper.  The  virtual  image  of  the 
sun  formed  by  a  double  concave  lens  can  not  be  projected  on 
paper.  It  has  no  real  existence  ;  it  is  an  optical  illusion.  It 
can  be  seen  at  F,  if  the  eye  is  placed  in  the  divergent  beam. 

Conjugate  Foci.  —  If  the  rays  passing  through  the 
double  convex  lens  proceed  from  a  point  0,  not  infinitely 
removed,  the  rays  will  diverge  upon  the  lens,  and  will  con- 
verge to  a  point  I,  which  is  farther  away  from  the  lens  than 
the  principal  focus.  If  0  moves  away  from  the  lens  to  an 

infinite  distance,  I 
will  move  up  to  the 
principal  focus  F.  If 
0  moves  up  to  the 
principal  focus,  I  will 
move  away  to  an  infinite  distance,  or  the  rays  will  emerge 
in  a  parallel  beam.  For  each  position  of  0,  there  will  be 
a  definite  position  of  its  image  I. 

In  all  these  cases,  if  the  radiant  point  0  be  placed  at  the  position 
occupied  by  the  image,  the  image  will  appear  at  the  former  position  of 
the  object.  The  object  and  image  have  changed  places,  and  the  light  re- 
traces its  former  path.  Points  thus  related  are  said  to  be  conjugate  foci. 

Foci  of  a  Double  Concave  Lens.  —  If  rays  diverge 
from  a  point  upon  a  double  concave  lens,  they  will,  on  leav- 

ing the  lens,  diverge 
more  widely  than  if 
they  had  entered  in 
a  parallel  beam.  To 
an  eye  placed  in  the 
divergent  beam,  the 


FIG.  201.— CONJUGATE  Foci. 


have  come  from  a  point  I,  which  is  nearer  the  lens  than 
the  principal  focus. 


IMAGES  BY  LENSES. 


325 


FIG.  203.— VIRTUAL  Foci  OF  A 
DOUBLE  CONVEX  LENS. 


The  two  points  occupied  by  the  object  and  its  image  are  not  con- 
jugate for  a  double  concave  lens. 

Virtual   Foci  of  a  Double  Convex   Lens. — If   the 

radiant  point  be  placed  nearer  to  the  lens  than  the  principal 
focus,  the  rays  will  diverge  after 
passing  through  the  lens.     The 
point  I,  from  which  they  seem 
to  have  diverged,  will  be  a  vir- 
tual focus.     The  nearer  the  ra- 
diant point  0  is  to  the  principal 
focus,  the  farther  I  will  be  from 
the  lens.     The  object  and  its  image  are  not  at  conjugate 
points  when  the  image  is  virtual. 

Formation  of  Images  by  Lenses. — Let  A  B  represent 
any  object.  If  rays  proceed  from  the  extremities  A  and  B 
through  the  optical  center,  they  pass  on  without  refraction. 
Such  rays  follow  the  line  of  the  secondary  axis.  The  image 
of  B  will  be  somewhere  on  the  secondary  axis  through  B. 
Draw  any  other  ray  from  B,  and  find  where  it  intersects  the 
secondary  axis  through 

B,  after  passing  the  lens.     |— -^^_ ^^  a 

This  intersection  will  lo- 
cate the  image  of  B,  since 
all  rays  diverging  from 

J  FIG.  204.— FORMATION  OF  IMAGE  BY  A  LENS. 

B  and  passing  through 

the  lens  will  converge  to  the  same  point.  Such  are  the  con- 
ditions under  which  an  image  will  be  formed,  reproducing 
the  object  in  shape  and  color. 

It  is  convenient  to  select,  as  the  second  ray  radiating  from  B,  that 
one  which  is  parallel  to  the  principal  axis.  This  ray  passes  through 
the  principal  focus,  F,  and  thence  on  until  it  intersects  the  secondary 
axis,  in  b.  Similarly,  rays  from  A,  on  passing  through  the  lens,  will 
converge  upon  the  secondary  axis  through  A  at  a.  Thus  the  image 
will  be  inverted. 

Evidently,  if  a  &  were  the  object,  A  B  would  be  the  image.  The 
object  and  image  may  change  places.  Or,  if  A  B  were  to  move  toward 


326  LIGHT. 

the  lens  until  its  distance  becomes  equal  to  the  present  distance  of  the 
image,  a  b  would  recede  until  its  distance  equals  the  present  distance 
of  the  object.  The  object  and  image  occupy  conjugate  foci.  The 
image  is  always  real  when  the  object  is  outside  of  the  principal  focus. 

Virtual  Image. — If  the  object  is  nearer  the  lens  than 
the  principal  focus,  the  image  will  be  virtual,  magnified,  and 
erect.  (See  Fig.  205.)  The  image  of  each  point  of  the  ob- 


FIG.  205.— MAGNIFIED  IMAGE  OF  HESSIAN  FLY  BY  CONVEX  LENS. 

ject  will  be  on  a  secondary  axis  through  that  point,  in  all 
cases,  whether  the  image  be  real  or  virtual. 

When  the  lens  is  used  as  in  Fig.  205,  it  is  called  a  simple  micro- 
scope. Pocket-lenses  and  reading-glasses  magnify  on  this  principle. 

Images  by  Concave  Lenses. — Images  formed  by  con- 
cave lenses  are  virtual,  erect,  and  diminished.  They  can  be 
seen  through  the  lens,  being  on  the  same  side  of  the  lens  as 
the  object. 

Can  you  draw  a  diagram  illustrating  the  path  of  rays  through  a 
double  concave  lens,  and  showing  why  the  image  is  reduced  I 

Spherical  Aberration. — The  rays  which  traverse  a 
converging  lens  near  the  margin  do  not  come  to  a  focus  at 

quite  the  same  point  as  those 
which  pass  through  the  cen- 
tral portion.  They  are 
more  refracted,  and  hence 
converge  at  a  point  F', 
FIG.  ^-SPHERICAL  ABERRATION  EX-  nearer  the  lens  than  the 

PLAINED.  .  . 

point  _b ,  at  which  the  more 

central  rays  meet.     This  causes  indistinctness  in  the  result- 
ing image.     To  render  it  sharp,  the  marginal  rays  may  be 


LAW  OP  INTENSITY  OF  LIGHT.  327 

cut  off  by  means  of  a  plate  with  a  circular  opening,  called 
a  diaphragm  (di'a-fram).  The  image  formed  by  the  cen- 
tral rays  thus  becomes  more  distinct,  but  it  is  less  bright. 
Spherical  mirrors  have  the  same  defect. 

Light  a  lamp,  and  with  your  reading-glass  illustrate  the  principle 
explained  above.  A  diaphragm  may  be  made  out  of  a  piece  of  card- 
board, and  the  central  rays  focused.  If  the  central  portion  of  the  lens 
be  covered  with  a  circular  piece  of  paper,-  the  marginal  rays  may  be 
focused.  Measure  the  focal  distance  in  each  case,  and  compare  the 
images  with  that  formed  by  the  entire  lens. 

Law  of  Intensity  of  Illumination. — The  images  from 
lenses  are  always  formed  in  a  fixed  position  when  the  posi- 
tion of  the  object  with  respect  to  the  lens  is  once  fixed. 
Moving  the  screen  upon  which  the  image  is  projected,  will 
throw  the  image  out,  of  focus. 

The  images  formed  by  a  small  opening  may  be  projected 
on  a  screen  at  any  distance  from  the  opening.  Doubling 
the  distance  of  the  screen  will  double  the  linear  dimensions 
of  the  image.  The  surface  covered  will,  therefore,  be  four 
times  as  large,  and  since  the  amount  of  light  streaming 
through  the  opening  is  the  same  in  each  case,  the  bright- 
ness of  the  image  in  the  second  position  will  be  one  fourth 
as  great  as  in  the  first.  The  same  principle  applies  to 
images  formed  by  lenses ;  they  vary 
in  brightness  inversely  as  the  squares  A  J3. 

of  the  focal  distances. 

This  law  may  be  illustrated  by  placing 
a  square  card  1  foot  from  a  candle,  as  in 

Fig.  207,  at  A.     It  receives  from  a  given 

,     FIG.  207.— LAW  OF  INTENSITY 
point   in   the  name  a  certain  amount  of  EXPLAINED 

light.     The  same  light,  if  not  intercepted 

at  A,  goes  on  to  B  at  a  distance  of  2  feet.  It  there  illuminates  four 
squares  of  the  same  size  as  the  card,  and  has,  therefore,  but  one  fourth 
of  its  former  intensity.  If  allowed  to  proceed  to  C,  3  feet,  it  illumi- 
nates nine  such  squares  and  has  but  one  ninth  of  its  original  intensity. 

Thus  the  intensity  of  light  diminishes  according  to  the 
square  of  the  distance  from  the  source  of  illumination. 


328 


LIGHT. 


QUESTIONS.— Describe  a  Prism.  Name  the  two  effects  of  prisms  on  light.  Ex- 
plain the  course  of  a  ray  of  light  through  a  prism.  What  can  you  say  of  the 
loss  of  light  by  repeated  reflection  ?  Define  Lenses.  Name  and  describe  each 
kind  of  lens.  What  is  the  center  of  curvature  of  a  lens  ?  The  normal  ?  The 
principal  axis  ?  The  secondary  axis  ?  The  principal  focus  ?  Distinguish  be- 
tween real  and  virtual  foci.  What  is  the  focal  length,  and  by  what  is  it  deter- 
mined ?  Explain  conjugate  foci. 

How  are  images  formed  by  lenses  ?  When  are  they  inverted  ?  Suppose  the 
object  to  be  nearer  a  convex  lens  than  the  principal  focus  ;  describe  the  image 
formed.  How  can  you  verify  this  with  your  simple  pocket  microscope  or 
reading-glass  ?  Describe  the  image  formed  by  concave  lenses.  What  is  Spher- 
ical Aberration  and  what  does  it  cause  ?  How  can  you  illustrate  it  ?  Demon- 
strate the  law  of  intensity  of  illumination. 


COLOR. 

Decomposition  of  Light  by  Prisms. — If  a  triangular 
prism  be  placed  in  the  path  of  a  slender  beam  of  light  (see 
Fig.  208),  instead  of  a  round,  white  image  of  the  sun,  we 


FIG.  808. — DECOMPOSITION  OF  WHITE  LIGHT  BY  TRIANGULAR  PRISM. 

observe  a  band  of  color.  The  light  is  refracted,  as  has  been 
already  explained,  but  it  is  not  all  equally  refracted.  At 
one  extremity  of  the  band,  or  spectrum,  the  light  is  violet ; 


RECOMPOSITION   OF   WHITE  LIGHT. 


329 


indigo,  blue,  green,  yellow,  orange,  and  red  succeed,  each 
imperceptibly  merging  into  that  which  follows. 

The  violet  light  is  most  refracted,  being  deflected  through 
the  angle  V  P  E,  while  the  red  light  is  deflected  through 
the  angle  R  P  E. 

The  band  of  color  is,  in  fact,  a  series  of  overlapping 
images  of  the  sun  (see  page  297).  These  images  can  be 
again  superposed  by  means  of  a  double  convex  lens,  as  is 
shown  in  Fig.  209.  The  resulting  image  is  white. 


FIG.  209.— RECOMPOSITION  OF  WHITE  LIGHT  BY  CONVEX  LENS. 

These  two  impressive  experiments  prove  that  the  white 
light  of  the  sun  is  composed  of  the  colors  seen  in  the 
spectrum. 

Prisms  of  Different  Material,  as  crown-glass,  flint- 
glass,  quartz,  rock-salt,  and  water,  having  the 
same  angle,  will  refract  light  unequally.  If  the 
angles  of  the  prisms  are  adjusted  so  that  they 
all  deviate  the  red  ray  through  equal  angles,  the 
violet  rays  will  still  be  deviated  through  differ- 
ent angles.  In  other  words,  the  spectra  will  have 
different  lengths.  Flint-glass  gives,  under  these  conditions, 
about  twice  as  long  a  spectrum  as  crown-glass. 


330 


LIGHT. 


CROWN  GLASS 


FLINT  GLASS 
FIG.  211.— ACHROMATIC  LENS. 


In  Fig.  210,  F  represents  a  prism  of  flint-glass,  and  C  one  of  com- 
mon glass,  whose  angles  are  so  adjusted  that  they  give  spectra  of  the 
same  length.  When  placed  as  shown  in  the  figure,  one  will  therefore 
neutralize  the  dispersive  effect  of  the  other,  and  the  emerging  beam 
will  be  white  light.  It  will,  however,  have  been  deviated  toward  the 
base  of  prism  C. 

Chromatic  Aberration. — A  combination  of  lenses  or 
prisms  in  which  dispersion  into  color  is  neutralized,  is  said 
to  be  achromatic.  Objects  seen  through  ordinary  lenses  are 
surrounded  by  a  fringe  of  color, 
which,  like  spherical  aberration, 
interferes  with  definition.  This 
arises  from  the  fact  that  rays  of 
different  colors  are  refracted  to 
different  foci,  involving  the  formation  of  a  number  of  images 
partly  overlapping  one  another.  The  defect  is  known  as 
chromatic  aberration,  and  is  corrected  by  combining  a  con- 
vex lens  of  crown-glass  with  a  concave  lens  of  flint-glass. 

Suppose  the  prisms  just  illustrated  were  of  the  same  material, 
when  would  they  become  achromatic  f  Would  there  then  be  deviation 
of  the  ray  f 

Spectrum  Colors  otherwise  combined.  —  The  re- 
refracted  light  from  a  prism  may  be  reflected  to  the  wall 

of  the  room  by  means  of 
a  hand  mirror.  Give  the 
mirror  a  rapid  motion  to 
and  fro.  Each  color  of 
the  spectrum  will  be 
drawn  out  into  a  band,  as 
in  the  case  of  a  point  of 
light  on  the  end  of  a  stick 
when  whirled  in  a  circle. 
If  the  mirror  is  so  moved 
that  these  bands  coincide, 

The  card  A  bears  the  seven  spectrum  colors,    the  resulting  band  Will  ap- 

reproduced  five  times.  pear  white  in  its  central 


FIG.  212.— NEWTON'S  DISK. 


COMBINATION  OF  SPECTRUM  COLORS.  331 

part,  where  all  the  colors  overlap.  Notice  that  the  ends  of 
the  band  are  colored,  and  explain  their  appearance. 

A  Newton's  Disk  consists  of  a  circular  piece  of  card- 
board, having  colored  sectors.  The  sectors  may  be  of  tinted 
paper,  pasted  on  a  card,  as  in  A,  Fig.  212.  If  the  disk  is 
spun  rapidly  round,  the  color  impressions  blend,  and  it  ap- 
pears of  a  grayish- white  color,  B.  (See  No.  2,  introductory 
cut,  page  293.) 

The  experiment  may  be  successfully  performed  if  the 
spectrum  colors  are  represented  on  the  disk  but  once,  in 
proper  proportion. 

In  the  experiments  just  described,  the  colors  are  combined  by  the 
persistence  of  vision.  At  any  given  instant,  the  image  of  each  sector 
is  formed  at  a  certain  point  on  the  retina  of  the  eye.  As  the  sector 
revolves,  its  image  moves  round  in  a  corresponding  path  upon  the 
retina,  returning  quickly  to  its  original  position.  During  this  rapid 
revolution,  the  sensation  produced  has  not  had  time  to  die  out,  and  the 
impression  therefore  appears  continuous.  The  rapid  recurrence  of  each 
colored  image  has  the  same  effect  as  a  simultaneous  impression  of  all. 

If  a  colored  sector  is  put  on  a  black  disk  and  the  disk  revolved, 
the  effect  will  be  that  of  the  color  diluted  with  black,  the  precise  ap- 
pearance depending  upon  the  relative  amounts 
of  colored  and  blackened  surface.      A  white 
diluted  with  black  will  give  gray,  which  is  a 
dull  white. 

Mixing   Colors    by   Reflection. — 

Place  two  rectangular  pieces  of  paper, 

one  yellow  and  the  other  blue,  upon  a 

black  surface.    Hold  a  strip  of  thin  glass, 

G  (see  Fig.  213),  so  that  the  reflected 

image  of  the  yellow  paper  seems  to  cover 

the  piece  of  blue  paper  seen  obliquely  BLUE  YELLOW 

through  the  glass.     The  resulting  color  FlG-  SIS.-COLORS  MIXED 

.,,  ,  .  BY  REFLECTION. 

will  be  a  mixture  of  the  two  tints. 

Vary  the  height  of  G  above  the  papers.  At  a  certain  distance  the 
mixture  will  appear  a  dull  white.  If  the  glass  is  raised  the  color  will 
be  yellowish,  and  if  depressed  it  will  be  bluish.  Why1? 


332 


LIGHT. 


Complementary  Colors. — All  the  colors  of  the  spec- 
trum, when  mixed  by  a  Newton  disk,  produce,  as  we  have 
seen,  a  white.  Remove  red  from 
the  disk,  and  the  remaining  colors 
will,  on  rotation,  give  a  bluish  green. 
Match  this  color  by  a  colored  paper, 
and  place  it  upon  the  disk  with  red. 
Rotate  the  disk,  and  the  result  will 
be  white.  In  the  same  way,  orange 
and  cyanogen  blue,  purple  and  green, 
will  yield  a  white.  In  Fig.  214, 
the  colors  which  are  shown  oppo- 
site one  another,  when  mixed  by  a 
Such  colors  are  called  Complementary 


GREEN 

FIG.  214. — COMPLEMENTARY 
COLORS. 


disk,  will  give  white. 
Colors. 

A  combination  of  red  and  green  in  different  proportions  will  pro- 
duce the  intermediate  colors— orange,  yellow,  and  yellowish  green. 
Prom  violet  and  green,  the  colors  bluish  green,  cyanogen  blue,  and 
ultramarine  blue  can  be  obtained ;  while  violet  and  red  give  purple. 
A  mixture  of  no  two  colors  will  produce  red,  violet,  or  green.  These 
are  therefore  called  primary  colors,  while  the  others  are  called  sec- 
ondary, as  they  all  can  be  obtained  by  mixing  the  primaries. 

The  eye  is  not  able  to  distinguish  between  the  white  produced  by 
mixing  all  the  colors  of  the  spectrum,  and  that  formed  from  any  two 
complementary  colors,  or  from  the  three  primary  colors.  In  this 
regard,  the  eye  has  less  power  of  analysis  than  the  ear.  When  a 
harmony  is  rendered,  the  ear  can  detect  each  of  the  simultaneously 
sounded  notes  of  every  instrument,  and  the  trained  ear  of  one  familiar 
with  the  music  can  single  out  any  instrument  in  the  orchestra,  and 
detect  an  error  in  the  playing. 

Color  of  Mixed  Pigments.— If  the  two  pigments 
known  as  chrome-yellow  and  Prussian-blue  be  mixed,  the 
result  will  be  a  green  pigment ;  but  the  mixture  of  yellow 
and  blue  light  will  produce  white  light. 

Blue  and  yellow  light  may  be  mixed  on  a  screen  by  means  of  two 
magic  lanterns,  plates  of  colored  glass  being  used  as  slides.  The 
experiment  is  a  very  striking  one,  as  shown  in  Fig.  215. 


MIXTURE  OF  LIGHT. 


333 


A  similar  experiment  may  be  made  with  yellow  and  blue  sheets 
of  gelatine.     Place  the  two  sheets,  Y  and  B,  Fig.  216,  side  by  side,  and 


FIG.  215. — MIXTURE  OF  BLUE  AND  YELLOW  LIGHT  ON  A  SCREEN. 

send  a  beam  of  white  light  through  each.  Allow  the  two  beams  of 
light  to  fall  upon  a  screen.  One  will  appear  yellow,  and  one  blue. 
If  the  colored  beams  be  passed  through  a  prism,  it  will  be  found  that 
the  blue  beam 
contains  green, 
blue,  and  violet, 
with  possibly  a 
trace  of  red. 
Yellow,  orange, 
and  most  of  the 
red,  have  been 
quenched.  The 
yellow  beam  has 
red,  orange,  yel- 
low, and  green ; 
the  blue  and  vio- 
let having  been 
quenched. 

If  the  yellow 
beam  be  reflected 

by   a   mirror,  M,       /    ^Q  216.— MIXTURE  OF  LIGHT  BY  GELATINE  SHEETS. 
Fig.  216,  so  that 

the  yellow  and  blue  are  combined  on  the  screen,  a  white  will  be  ob- 
tained.    All  the  spectrum  colors  will  be  combined,  and  in  approxi- 


334 


LIGHT. 


mately  the  same  proportion  as  in  sunlight.    The  action  of  the  gela- 
tines is  represented  by  cancellation,  as  follows : 

Blue  gelatine,  •      j^,  ty  X  &  B  I  U 
Yellow  gelatine,      R  0  Y  G  ^  \  ^ 

In  Fig.  217,  the  light  is  passed  successively  through  the 
two  gelatines.  The  green,  with  perhaps  a  trace  of  red,  is 

the  only  light 
which  can  pass 
through  both, 
and  this  red 
with  its~  equiva- 
lent green  gives 
white.  The  re- 
sult is  to  make 
a  lighter  green. 

FIG.  217.— BEAM  PASSING  THROUGH  GELATINE  SHEETS  AND  The  blue  2"el- 

FALLING  ON  SCREEN.  ° 

atme  may  be  re- 
placed by  a  cell  of  copper-sulphate  solution,  and  the  yellow 
gelatine,  by  a  potassium-bichromate  solution. 

If  the  gelatines  gave  pure  yellow  and  blue  lights,  the  result  of 
their  combination,  as  in  Fig.  217,  would  be  darkness,  and  not  green. 
The  yellow  gelatine  would  transmit  only  yellow  light.  This  would  be 
quenched  by  the  blue  gelatine,  which  would  transmit  only  blue. 

Color  of  Bodies. — When  white  light  falls  upon  a  body, 
a  portion  of  it  is  reflected  from  the  outer  surface.  This 
light  is  white,  as  may 
be  seen  by  reflecting 
sunlight  from  an  un- 
ground  colored  glass 
(Fig.  218).  Some  rays 
are  reflected  from  the 
first  surface.  These 
are  not  drawn  in  the 
figure.  Part  of  the  light 
enters  the  glass,  and,  being  reflected  from  the  lower  surface, 
again  emerges,  and  may  fall  upon  the  walls  of  the  room. 


b       m 

FIG.  218. — REFLECTION  OF  LIGHT  FROM  GLASS. 


COLOR  OF  BODIES.  335 

An  irregularity,  like  that  shown  greatly  exaggerated  at  b  m, 
would  disperse  the  light,  leaving  a  gap,  as  a  c,  in  the  reflec- 
tion on  the  wall.  Here  the  white  light  from  the  upper 
surface,  from  such  rays  as  those  marked  1,  2,  3,  4,  will  be 
observed. 

So  in  all  colored  bodies,  the  colored  light  comes  from 
the  interior  of  the  body,  where  it  has  been  reflected  from 
facets  slightly  below  the  surface.  The  color  is  due  to  light 
aot  quenched  by  the  body. 

When  a  blue  and  a -yellow  pigment  are  mixed,  green  is  the 
only  light  which  penetrates  slightly  below  the  eurface,  and  is  re- 
flected out  again,  unquenched.  If  the  pigments  which  artists  use 
were  all  pure  colors,  a  mixture  of  any  two  would  give  black,  which 
would  appear  grayish  on  account  of  the  white  light  reflected  from 
the  surface. 

When  light  is  quenched  within  a  body,  it  is  because  the 
energy  of  vibration  is  used  in  setting  the  molecules  of  the 
body  into  motion.  The  body  is  heated. 

The  Color  of  Bodies  thus  depends  upon  their  mo- 
lecular structure.  Different  bodies  quench  different  por- 
tions of  the  complex  solar  light.  The  unquenched  light 
determines  their  color. 

The  color  of  bodies  also  depends  on  the  light  which  falls  upon 
them.  If  a  loose  bunch  of  candle-wick  be  moistened  with  strong  brine 
and  then  with  alcohol,  it  will,  if  ignited,  give  a  pure  yellow  flame, 
called  the  sodium  flame.  It  contains  no  red,  green,  or  blue  light.  In 
a  room  illuminated  only  by  this  light,  the  red  flowers  and  green  leaves 
of  a  geranium  or  rose  look  exactly  alike,  being  a  dark  gray.  A  stick 
of  red  sealing-wax  appears  dark  brown  or  black.  These  bodies  can 
not  reflect  yellow  light.  In  a  dark  room,  all  things  are  black,  or  with- 
out color. 

The  clouds  sometimes  quench  unusual  portions  of  the  sunlight, 
and  all  the  hues  of  the  landscape  are  changed.  During  storms,  these 
changes  often  take  place  rapidly.  The  morning  and  evening  sunlight 
contains  less  of  the  violet  end  of  the  spectrum  than  the  noon  sunlight, 
as  the  light  travels  a  longer  distance  in  air,  in  which  the  yellow  and 
red  rays  are  less  affected  than  the  others. 


336  LIGHT. 

The  Color-Sense  and  Color-Blindness. — Finally,  the 
color  of  bodies  depends  upon  the  eyes  of  the  observer.  We 
can  not  describe  our  color  sensations  to  one  another.  We 
are  taught  that  the  grass  is  green,  the  rose  red ;  but  it  is 
probable  that  no  two  persons  see  colors  alike,  although  they 
apply  the  same  names  to  them.  There  are,  in  fact,  many 
who  can  not  distinguish  a  red  or  a  scarlet  from  a  drab  or 
brown.  To  such  persons,  a  pink  rose  has  the  same  appear- 
ance as  it  does  to  the  normal  eye  when  seen  by  moonlight. 
They  are  said  to  be  color-blind  to  red. 

Color-blindness  is  the  result  of  some  disease  or  congenital  defect 
in  the  nerves  of  the  eye ;  it  does  not  necessarily  interfere  with  keenness 
of  vision.  Blindness  for  all  colors  is  rare.  A  patient  totally  color- 
blind would  be  unable  to  distinguish  between  the  red  and  white  stripes 
in  our  flag,  or  the  blue  background  and  its  white  stars. 

Color  Fatigue. — We  may  readily  convince  ourselves 
that  our  own  impressions  of  color  are  continually  changing. 

Cover  the  lower  half  of  a  sheet  of  white  paper  with  a 
black,  lusterless  cloth.  Let  a  strong  light  fall  on  the  paper. 
Fix  the  eyes  steadily  upon  some  point  in  the  boundary  be- 
tween the  white  and  the  black  for  about  a  minute.  Then, 
without  moving  the  eyes,  withdraw  the  black  cloth.  The 
upper  portion  of  the  paper  will  appear  a  dull  gray,  in  com- 
parison with  the  section  just  uncovered,  because  that  part 
of  the  retina  upon  which  the  brighter  image  was  formed 
has  become  less  sensitive.  Ordinarily,  we  do  not  notice 
such  changes,  as  they  go  on  gradually,  and  we  have  no 
means  of  simultaneous  comparison. 

The  white  paper  may  be  replaced  by  red.  This  will 
look  dull  after  a  minute  of  exposure  to  the  eye,  while  the 
freshly  uncovered  red  will  appear  strong,  because  its  image 
falls  upon  an  unfatigued  part  of  the  retina. 

When  the  eye  is  fatigued  for  red,  all  other  compound 
colors  will,  until  the  eye  recovers,  appear  as  if  red  had  been 
stricken  out  of  them.  White  will  appear  greenish,  green 
appear  intensified. 


MUTUAL  EFFECT  OF  COLORS.  337 

EXPERIMENTS. — Look  at  a  strongly  illuminated  red  on  a  black 
ground ;  then  turn  the  eyes  to  a  white  wall.  You  will  observe  an 
after-image  of  the  red  spot,  which  will  appear  green.  If  the  eyes  be 
directed  to  a  green  paper,  instead  of  the  white  wall,  the  after-image 
will  appear  a  more  intense  green. 

Look  at  a  bright  object,  like  a  white  cloud,  through  a  green  glass, 
with  one  eye,  and  through  a  red  glass  with  the  other.  After  a  time, 
transfer  both  eyes  to  one  glass,  and  open  and  close  them  alternately. 

Look  at  objects  through  a  red  glass,  with  one  eye,  then  through  a 
green  glass  with  the  other;  then  look  through  both  simultaneously. 
In  which  case  do  objects  seem  to  have  most  nearly  their  natural  colors  ? 

When  their  eyes  are  fresh,  artists  are  frequently  dissatis- 
fied with  work  done  when  their  eyes  were  fatigued. 

Mutual  Effect  of  Colors. — Paste  one  circular  piece  of 
green  paper  on  the  center  of  a  gray  card-board,  and  another 
on  the  center  of  a  red  one.  The  green  surrounded  by  red 
will  seem  much  stronger.  The  red  also  appears  stronger 
than  it  would  if  the  green  were  absent. 

Fix  the  eye  upon  the  center  of  the  green  disk  surrounded  by  red. 
At  the  same  time,  notice  the  colors  at  the  boundary  between  the  red 
and  the  green.  Both  colors  seem  stronger  there  than  at  some  distance 
away.  The  fatiguing  effect  for  red  or  green  extends  beyond  the  geo- 
metrical boundary  of  the  images  on  the  retina,  and  hence  each  color  is 
intensified  by  the  juxtaposition  of  the  other. 

QUESTIONS.— Explain  the  decomposition  of  white  light  by  a  prism.  What  kind  of 
light  is  most  refracted  ?  Prove  that  white  light  is  a  mixture  of  all  colors.  Ex- 
plain what  is  meant  by  chromatic  aberration,  and  show  how  it  is  corrected. 
How  may  the  spectrum  colo'rs  be  combined  by  a  Newton's  disk  ?  Account  for 
the  persistence  of  vision  in  all  such  cases. 

How  may  colors  be- mixed  by  reflection  ?  By  the  use  of  two  lanterns  ?  By  gela- 
tine sheets  ?  Why  do  we  not  obtain  the  same  results  by  mixing  colored  lights 
as  by  mixing  pigments  ?  What  are  complementary  colors  ? 

On  what  does  the  color  of  bodies  primarily  depend  ?  Follow  the  course  of  a  ray 
of  white  light  falling  on  a  piece  of  colored  glass.  Why  is  the  color  of  a  body 
determined  by  light  reflected  from  the  interior  ?  When  light  is  quenched  within 
a  body,  is  heat  generated  ?  Why  ?  How  far  is  the  color  of  bodies  dependent 
upon  the  character  of  the  light  in  which  they  are  seen  ?  Why  is  a  violet  blue  ? 
A  calla-lily,  white  ?  Why  are  sunsets  characterized  by  red  and  yellow  tints  ? 
When  is  a  substance  black  ?  What  is  white  ?  What  is  black  ?  Is  either  a 
color  ?  Which  reflects  the  most  light  ?  The  most  heat  ?  Why  are  whites  and 
straw-colors  seasonable  in  summer  ?  Dark-colored  fabrics  in  winter  ? 

How  important  a  factor  is  the  color-sense  of  the  individual  in  the  discrimination 
of  colors  ?  Describe  color-blindness  ?  What  is  color-fatigue  ? 


LIGHT. 


FIG.  219.— PRINCIPLE  OP  THE  SPECTROSCOPE. 


THE  SPECTROSCOPE  AND  SPECTRUM  ANALYSIS. 

The  Spectroscope  is  an  instrument  used  for  the 
analysis  of  light.  It  consists  of  one  or  more  prisms  for 
the  production  of  the  spectrum,  and  a  telescope  for  examin- 
ing it. 

The  light  is  admitted  to  the  prism  through  a  narrow  slit,  S,  in  the 
end  of  the  tube  A  (see  Fig.  219),  and  then  through  a  lens  at  the  op- 
posite end  of  this  tube.  The  principal  focus  of  the  lens  is  at  the  slit. 

The  light  radiat- 
ing from  the  slit 
upon  the  lens 
is  rendered  par- 
allel, and  pass- 
es through  the 
prism  to  the  tel- 
escope, B,  which 
is  first  focused 

upon  the  slit.     Instead  of  the  sun  as  a  radiant  object,  the  illuminated 
slit  is  thus  used. 

The  light  has  been  deviated  through  the  angle  b  a  e,  which  is 
measured  by  means  of  a  divided  circle  on  the  bed-plate,  B'.  The  tele- 
scope swings  round  the  center  a,  and  is  first  set  in  the  line  a  b,  being 
focused  on  the  slit 
when  the  prism  is 
removed.  When  the 
prism  is  returned  to 
its  place,  the  tele- 
scope must  occupy 
the  position  shown 
at  B  in  Fig.  219,  in 
order  that  the  ob- 
server may  see  the 
slit,  which  now  ap- 
pears widened  out 
into  a  band  of  col- 
or,— the  spectrum.  FIG.  220.— THE  FOUR- PRISM  SPECTROSCOPE. 

Fig.  220  shows  a  form  of  spectroscope  in  which  four 
prisms  are  used.  Each  prism  increases  the  deviation  and 


PRINCIPLE  OF  THE  SPECTROSCOPE. 


339 


dispersion  of  the  light.  Entering  the  slit  in  tube  A,  the 
width  of  which  can  be  regulated  by  a  screw,  the  light  is 
bent  round  the  train  of  prisms,  and  thrown  back  into  the 
telescope  B,  being  almost  reversed  in  direction. 

If  the  light  from  a  white-hot  solid  or  liquid  body  be 
examined  with  a  spec- 
troscope, a  continuous 
band  of  all  colors  from 
red  to  violet  is  observed 
(as  shown  in  Fig.  221). 

When  the  glowing  body 
is  in  the  form  of  a  gas  or 
vapor,  a  different  kind  of 
spectrum  is  seen.  For  in- 
stance, if  the  yellow  light  of 
sodium  vapor  be  observed,  the  spectrum  consists  only  of  a  slender 
beam  of  yellow  light.  Not  only  is  that  part  of  the  spectrum  corre- 
sponding to  red,  orange,  green,  blue,  and  violet,  wholly  wanting,  but 
the  greater  part  of  the  yellow  seen  in  a  continuous  spectrum  of  a 
white-hot  solid  is  also  blank.  The  yellow  light  of  glowing  sodium 
vapor  is  thus  a  very  definite  kind  of  yellow. 

When  the  spectroscope  is  strong  enough,  it  is  distinctly  shown 
that  there  are  two  slender  beams  of  yellow  light,  very  close  together. 


FIG.  221.— THE  CONTINUOUS  SPECTRUM. 


FIG.  222. — THE  SPECTRUM  OF  SODIUM. 


FIG.  223.— SODIUM  LINES. 


By  means  of  each  of  these  beams,  a  sharp  image  of  the  slit  is  observed, 
the  images  being  separated  by  a  dark  space.  The  lower  part  of  Fig.  223 
shows  these  two  bright  lines.  They  are  also  indicated  at  I),  Fig.  224. 

Other    Bright-line    Spectra. — Iron    vaporizes   when 
placed  in  the  flame  of  an  electric  light.     The  light  from 


340 


LIGHT. 


the  glowing  vapor,  when  passed  through  the  slit  of  the 
spectroscope,  shows  a  spectrum  composed  of  hundreds  of 
slender  beams  from  red  to  violet,  all  separated  by  dark 
spaces.  By  means  of  each  of  these  beams,  a  narrow  image 
of  the  slit  is  seen,  appearing  as  a  bright  line. 

Every  substance,  when  in  a  condition  of  glowing  vapor,  gives  a 
bright-line  spectrum  on  a  dark  background.  As  these  spectra  differ 
in  the  number  and  position  of  their  lines,  we  are  enabled  to  identify 


FIG.  224.— COINCIDENCE  OF  THE  SPECTRUM  OF  IRON  WITH  65  OF  THE  DARK  LINES 
OF  THE  SOLAR  SPECTRUM. 

substances  by  means  of  the  spectroscope.  The  appearance  of  the  iron 
spectrum,  as  seen  in  an  instrument  of  moderate  power,  is  shown  in 
the  lower  part  of  Fig.  224. 

The  continuous  spectrum,  as  seen  in  the  spectroscope,  is  simply  a 
series  of  overlapping  images  of  the  slit. 

The  Solar  Spectrum. — When  sunlight  is  examined  by 
a  spectroscope,  a  band  of  color  is  seen ;  but  when  the  tele- 
scope is  focused  on  the  slit,  the  spectrum  appears  crossed 
by  hundreds  of  dark  lines,  as  shown  in  the  upper  part  of 
Fig.  224.  Two  of  these  dark  lines  are  in  the  yellow,  exactly 
where  the  two  sodium  lines  occur.  They  are  shown  at  D 
in  Fig.  224,  and  in  the  upper  part  of  Fig.  223.  Thus  our 
sunlight  appears  to  be  lacking  in  the  kind  of  light  which 
glowing  sodium  vapor  emits. 

So,  also,  the  bright  iron  lines  have  each  a  representative 
line  in  the  solar  spectrum  ;  but  they  are  dark  lines,  suggest- 
ing that  the  light  which  glowing  iron  vapor  emits  is  lacking 
in  our  sunlight.  These  two  spectra  can  be  produced  at  the 
same  time.  One  shows  a  band  of  color  with  dark  lines ; 


DARK  LINES  OF  THE  SPECTRUM.  341 

the  other  is  a  spectrum  of  bright  lines,  each  of  which  is 
exactly  opposite  a  dark  line  of  the  solar  spectrum. 

Fig.  224  shows  some  of  the  lines  of  iron,  and  their  coincidence 
with  dark  lines  in  the  sun's  spectrum,  the  solar  spectrum  being  above 
that  of  the  iron  spectrum. 

The  Dark  Lines. — We  might  at  first  think  that  the 
apparent  lack  of  sodium  light  in  the  sunlight  shows  the 
absence  of  sodium  in  the  sun.  This  conclusion  would  be 
hasty  and  incorrect. 

Focus  the  telescope  on  the  solar  spectrum  when  the  sunlight  is 
strong.  Then  place  a  Bunsen  flame  in  front  of  the  slit,  and  insert  in 
the  flame  a  piece  of  platinum  sheet  moistened  with  brine.  The  Bunsen 
flame  may  be  replaced  by  a  loose  bunch  of  candle-wick,  or  old  muslin 
torn  into  strips,  moistened  first  with  brine,  then  with  alcohol,  and 
ignited.  If  the  sunlight  be  cut  off,  the  bright  line  of  sodium  will  be 
observed;  if  the  sunlight  be  admitted,  this  line  will  become  dark. 

Now,  if  the  sodium  flame  be  alternately  placed  before  the  slit  and 
removed,  it  will  be  found  that  the  dark  line  is  made  darker  by  inter- 
posing the  yellow  sodium  flame.  A  cloud  passing  over  the  sun  may 
dim  the  brightness  of  the  solar  spectrum.  The  dark  sodium  line  will 
then  become  bright,  if  the  sodium  flame  be  kept  before  the  slit. 

It  is  thus  proved  that  the  dark  lines  of  the  solar  spec- 
trum are  really  bright.  They  appear  dark  by  contrast  with 
the  brighter  adjacent  portions  of  the  spectrum. 

If  the  sun  were  an  intensely  glowing  solid  or  liquid  mass,  it  would 
give  a  continuous  spectrum,  without  either  bright  or  dark  lines. 

But  suppose  this  glowing  mass  to  be  surrounded  by  an  atmosphere 
containing  cooler  (although  brilliant)  sodium  vapor.  This  vapor  would 
absorb  light  of  the  same  kind  as  it  emits,  and  hence  a  dark  line  would 
be  left  in  the  spectrum.  As  the  previous  experiment  shows,  we  can 
even  increase  this  absorption,  by  causing  the  sun's  light  to  pass  through 
more  sodium  vapor  placed  in  front  of  the  spectroscope  slit. 

Such  considerations  show  that  sodium,  iron,  and  many  other  sub- 
stances which  we  have  on  the  earth,  are  present  as  vapor  in  the  at- 
mosphere of  the  sun  and  stars. 

A  Similar  Case  of  Absorption. — Sweep  a  violin  string 
with  a  bow,  and  at  the  same  time  slide  the  finger  along  the 
string,  changing  the  note  from  the  fundamental  to  the 


34:2  LIGHT. 

highest  note  of  which  the  string  is  capable.  An  infinite 
number  of  notes  will  have  been  successively  produced.  If 
all  these  notes  were  simultaneously  produced,  we  should 
have  a  complex  sound  similar  to  the  complex  light  of  a 
white-hot  body,  having  color  ranging  from  red  to  violet. 

Imagine  this  complex  sound  to  proceed  along  a  hall-way  across 
which  are  stretched  a  multitude  of  wires,  all  attuned  in  unison  to 
some  definite  pitch.  The  sound-waves  in  unison  with  these  wires 
would  largely  exhaust  themselves  in  setting  the  wires  in  motion,  while 
the  waves  not  in  unison  would  pass  through  unchecked.  The  complex 
sound  after  passing  through  the  wires  would  be  lacking  in  precisely 
the  sound  which  the  wires  produce  if  they  are  set  in  motion.  If  an 
adjustable  resonator  were  used  to  analyze  this  complex  sound  (see 
page  404),  it  would  be  silent  when  adjusted  to  the  pitch  of  the  absorb- 
ing wires,  and  would  give  a  loud  response  if  its  length  were  made 
greater  or  less. 

It  is  thus  that  the  molecules  of  sodium  vapor  in  the  solar  at- 
mosphere quench  the  same  kind  of  light  which  they  would  give  off  if 
more  strongly  heated. 


QUESTIONS.— Explain  the  principle  of  the  spectroscope.  Describe  the  four-prism 
spectroscope.  Can  artificial  light  be  diffused  by  a  prism  ?  Is  the  spectrum 
formed  always  the  same  as  that  of  the  sun  ?  Illustrate  in  the  case  of  sodium 
vapor  ;  in  the  case  of  the  glowing  vapor  of  iron.  How  may  substances  be 
identified  by  means  of  the  spectroscope  ? 

Describe  the  Solar  Spectrum.  Account  for  the  dark  lines.  Why  would  it  be  in- 
correct to  argue  that  the  apparent  absence  of  the  characteristic  light  of  any 
element  in  the  sunlight  proves  the  absence  of  that  element  in  the  sun  ?  Cite  an 
experiment  in  point.  Are  the  dark  lines  really  dark  ?  How  may  they  be  the 
result  of  absorption  of  light  ?  State  a  similar  case  of  absorption  of  sound.  Of 
what  does  the  spectroscope  show  the  heavenly  bodies  to  be  composed  ? 


EFFECTS  OF  THE  SOLAR  RAY. 

The  Solar  Kay  exerts  different  effects  upon  different 
organs.  Falling  upon  the  retina  of  the  eye,  it  produces  the 
sensation  of  light,  and  different  parts  of  the  solar  spectrum 
excite  sensations  of  different  colors.  Its  effect  upon  the 
sensory  nerves  of  the  body  is  to  cause  the  sensation  of  heat. 
These  nerves,  however,  can  not  distinguish  between  red 


EFFECTS  OF  THE  SOLAR  RAY.  343 

rays  and  violet  rays,  but  only  very  crudely  between  rays  of 
greater  or  less  energy. 

Invisible  Solar  Bays. — In  like  manner,  by  far  the 
greater  part  of  the  solar  spectrum  is  imperceptible  to  the 
eye.  The  spectrum  extends  somewhat  beyond  the  violet 
and  very  far  beyond  the  red.  The  existence  of  the  invisible 
parts  of  the  spectrum — the  ultra-violet  and  infra-red. — is 
proved  by  other  means  than  the  effect  upon  the  eye.  For 
example,  the  salts  of  silver  will  blacken  in  the  dark  rays  be- 
yond the  violet,  and  delicate  instruments  for  indicating  heat 
show  marked  heat  effects  for  several  spectrum  lengths  be- 
low the  red. 

The  instrument  best  adapted  for  these  heat  measurements  is  a 
slender  strip  of  platinum,  which  is  placed  transversely  across  the 
spectrum  and  can  be  moved  from  one  end  to  the  other.  By  means  of 
proper  instruments,  the  electrical  resistance  of  this  platinum  strip  is 
measured.  This  resistance  increases  as  the  strip  is  warmed,  and  dimin- 
ishes as  it  is  cooled.  Every  dark  line  in  the  visible  spectrum  is  found 
to  be  a  cold  line.  When  the  instrument  is  moved  far  out  into  the 
ultra-red,  the  temperature  falls  as  it  passes  through  cold  lines  and 
bands,  and  rises  when  it  encounters  the  warmer  radiations  that  bound 
these  on  either  side,  all  being  wholly  invisible. 

Solar  Light  is  essential  to  Vegetable  Life  ;  plants 
deprived  of  it  wither  and  die.  It  is  believed  that  the  en- 
ergy exhibited  in  the  growth  of  plants  is  directly  traceable 
to  the  green  coloring-matter  which  occurs  as  grains  in  their 
cells,  and  which  by  absorbing  rays  of  light  transforms  the 
energy  residing  in  the  molecules.  The  infra-red  or  heat 
rays  are  also  an  important  factor  in  this  process ;  but  ger- 
mination is  furthered  principally  by  the  ultra-violet  rays, 
which,  by  a  provision  of  Nature,  are  in  excess  in  the  spring. 

Chemical  Effect  of  Sunlight. — If  the  dampers  of  a 
piano  are  raised  and  a  given  note  sung,  the  string  in  uni- 
son will  respond.  No  other  string  will  do  so.  Persons 
with  powerful  voices  have  been  known  to  shatter  a  glass 
vessel  by  singing  into  it  the  note  which  it  would  yield  if 


344 


LIGHT. 


The  Photographer's  Camera 

matic  lens    mounted    in   a  wooden 


struck.  Similarly,  light-waves,  beating  upon  certain  sub- 
stances, throw  the  molecules  into  a  vibration  sufficiently 
violent  to  shake  them  asunder.  This  is  called  a  chemical 
change,  and  explains  the  fading  of  colors  in  sunlight.  Sil- 
ver compounds  are  particularly  sensitive  to  decomposition 
by  the  blue  and  violet  rays. 

Photography  depends  upon  this  chemical  action  of  light,  an  image 
formed  by  lenses  being  received  on  a  sensitive  film  of  iodide  and  bro- 
mide of  silver  exposed  in  a  camera  obscura  (dark  chamber).  The  sil- 
ver salts  are  chemically  affected  by  the  strong  lights  and  shadows  of 
the  picture,  so  that  the  latter  may  be  developed  by  a  second  oper- 
ation. 

consists  of  an  achro- 
box,   at  the  back   of 
which  is  a  ground- 
sflass   plate    for   the 

O  Jr 

reception  of  the  im- 
age projected  by  the 
lens  (see  Fig.  225). 
This  image  is  real, 
inverted,  and  usually 
smaller  than  the  ob- 
ject, and  is  visible  on 
the  ground  glass  to 
the  operator.  In  or- 
der to  facilitate  fo- 
cusing, the  lens  is  usually  movable  in  the  brass  tube,  and  the 
camera  is  provided  with  a  rubber  or  cloth  bellows  by  means 
of  which  the  ground-glass  plate  may  be  pushed  backward 
and  forward.  When  a  focus  is  obtained,  the  ground-glass 


FIG.  2-25.— CAMERA  Box  AND  TUBE. 


NOTE.— The  chemistry  of  photography  is  fully  explained  in  the  manuals  of 
instruction  issued  by  all  reputable  dealers  in  photographic  materials.  It  ie  no 
longer  difficult,  to  become  an  expert  photographer.  The  Scovill  &  Adams  Com- 
pany, of  New  York,  furnishes  outfits  at  prices  within  the  reach  of  all ;  and  the 
young  pupil,  equipped  with  a  camera  and  dry  plates,  can  intelligently  investi- 
gate both  interesting  phenomena  of  light  and  the  chemical  processes  associated 
with  one  of  the  most  fascinating  of  arts. 


PHOTOGRAPHY.  345 

screen  is  removed,  and  a  plate-holder  containing  a  sensitized 
glass  plate  is  slipped  into  its  place. 

When  object  and  image  are  equally  distant  from  the  lens,  they  are 
of  the  same  size.  If  the  object  is  brought  nearer,  the  image  is  en- 
larged, and  in  photographing  from  the  microscopic  field  it  is  greatly 
exaggerated.  Features  invisible  to  the  naked  eye  are  thus  magnified 
and  photographed  in  the  Photo-Micrographic  Camera. 

Microscopic  photographs,  or  representations  of  large  objects  great- 
ly reduced,  are  also  made  on  glass  of  a  size  so  small  as  to  be  visible 
only  through  a  powerful  magnifier.  Small  lenses  of  short  focal  length 
are  employed  to  form  images  of  microscopic  minuteness.  The  contents 
of  10,000  volumes  might  in  this  way  be  so  materially  reduced  as  to  be 
contained  in  a  single  drawer,  but  the  photographs  would  have  to  be 
read  through  a  microscope.  Pages  have  been  concentrated  on  a  sur- 
face, one  inch  square,  and  during  the  last  siege  of  Paris  trained  pigeons 
carried  to  and  from  the  city  long  dispatches  thus  reduced. 

In  good  cameras,  spherical  and  chromatic  aberration 
are  corrected  by  combining  crown  and  flint  glass  in  the 
lenses,  and  by  the  use  of  diaphragms. 

The  principle  of  the  camera  obscura  is  utilized  by  the  draughts- 
man, A  mirror  is  employed  to  reflect  the  landscape  to  a  lens  mounted 
in  the  top  of  a  suitable  camera  ;  the  rays  are  thus  brought  to  a  focus 
on  a  sheet  of  paper,  forming  a  distinct  image  which  can  be  readily 
traced  with  a  pencil.  The  camera  is  large  enough  to  admit  the  upper 
part  of  the  draughtsman's  person,  a  dark  curtain  excluding  all  light 
except  what  enters  from  above.  A  small  tent  supported  by  a  tripod  is 
sometimes  used,  enabling  the  artist  to  sit  at  a  table  within. 

QUESTIONS.— Illustrate  the  different  effects  of  the  solar  ray  on  the  retina  ;  on  the 
nerves  of  the  body  ;  on  germination  and  the  growth  of  plants.  Can  the  sen- 
sory nerves  distinguish  between  red  heat  rays  and  violet  heat  rays  ?  What 
parts  of  the  spectrum  are  invisible  to  the  eye  ?  Describe  an  instrument  adapted 
to  measuring  heat  in  the  spectrum.  How  can  you  prove  the  existence  of  the 
invisible  solar  rays  ? 

How  may  a  glass  vessel  be  shattered  by  sound  vibrations  ?  Similarly,  describe  the 
principle  of  chemical  change  by  light ;  the  fading  of  colors.  What  is  the  action 
of  light  on  silver  salts  ?  Describe  minutely  the  photographer's  Camera,  and  the 
process  of  Photographing.  When  are  object  and  image  of  the  same  size  here  ? 
Explain  the  purpose  of  the  Photo-micrographic  Camera :  the  uses  of  micro- 
scopic photography.  Describe  the  draughtsman's  camera. 


346 


LIGHT. 


CILIA 

MUSCLE 


FIG.  226.— SECTION  OF  THE  HUMAN  EYE. 


THE  EYE.— MECHANISM  OF  VISION. 

The  Human  Eye  is  a  camera.  Its  outer  envelope  is 
quite  fibrous  and  rigid,  serving  as  a  protection  for  the  re- 
fracting structures  within.  It  is  called  the  white  of  the  eye, 
or  the  sclerotic  coat  (see  Fig.  226),  gives  attachment  to  the 

muscles  that  move  the  ball, 
and  is  connected  with  the 
dark-colored  choroid  coat 
which  makes  the  chamber 
of  the  eye  a  camera  ob- 
scura.  In  front,  we  have 
the  transparent  cornea,  the 
colorless  and  transparent 
aqueous  humor  of  the  an- 
terior chamber,  and  the 
elastic  crystalline  lens  sus- 
pended in  its  capsule  by 
the  suspensory  ligament.  The  glassy,  jelly-like  vitreous  hu- 
mor fills  the  posterior  cavity.  These  structures  serve  to 
form  a  real  and  inverted  image  of  external  objects  on  a 
delicate  nervous  membrane  called  the  retina,  which  lines 
the  choroid  coat  at  the  back  of  the  eye.  The  nerve-fibers 
of  the  retina  gather  into  the  optic  nerve,  the  medium  of 
communication  with  the  brain. 

Spherical  aberration  is  in  part  avoided  in  the  eye  by  the  curva- 
ture of  the  retina,  and  through  the  cutting  off  of  marginal  rays  by  a 
movable  diaphram  called  the  iris.  It  is  the  color  of  this  diaphram 
which  determines  the  color  of  the  eye.  The  aperture  in  the  center  is 
called  the  pupil.  The  iris  automatically  regulates  the  size  of  the 
pupil,  and  hence  the  amount  of  light  admitted  to  the  eye-ball. 

The  Eyes  Move  through  a  considerable  angle  in  their 
sockets  in  order  that  they  may  be  directed  upon  any  object. 
Accurate  seeing  is  done  only  by  a  minute  spot  on  the  retina, 
called  the  yellow  spot. 


ACCOMMODATION.  347 

Fix  the  eye  upon  the  middle  of  a  line  of  this  page  and  you  will 
find  yourself  unable  to  read  the  whole  line  without  moving  the  eyes. 
You  have  the  power  to  direct  the  eye  from  the  bottom  to  the  top  of  a 
letter,  the  object  of  the  act  being  merely  to  bring  the  image  of  the 
point  to  be  observed  upon  the  sensitive  spot. 

When  the  sky  is  clear,  the  planet  Venus  is  usually  visible  at  mid- 
day. It  is,  however,  very  difficult  to  find  the  planet,  although  it  is 
distinctly  seen  when  found.  This  shows  that  the  sensitive  spot  is  ex- 
tremely small. 

Accommodation. — The  eye,  like  the  camera,  requires 
to  be  focused  for  objects  of  varying  distance.  This  is  ac- 
complished mainly  by  a  change  in  the  curvature  of  the 
front  of  the  lens,  accom- 
panied with  a  correspond- 
ing increase,  for  a  near  ob- 
ject, of  the  existing  refrac- 
tion of  the  eye  (see  Fig. 
227).  The  eye  is  repre- 
sented in  a  state  of  rest  in 
the  right  half  of  the  dia- 
gram, and  in  strong  ac- 
commodation for  near  vis-  Fia  ^--CONDITION  OF  EYE  AT  REST  AND 

IN  STRONG  ACCOMMODATION. 

ion   on    the  left.       It    is 

through  this  power  of  accommodation  that  we  are  enabled 

to  see  distinctly  both  near  and  distant  objects. 

Looking  at  a  near  object  requires  a  fatiguing  effort  of  the  ciliary 
muscles  (see  Fig.  226),  which  relax  the  suspensory  ligament,  allowing 
the  elastic  lens  to  become  more  convex.  The  eye  is  rested  by  fixing  it 
on  a  distant  object. 

Single  Vision  with  Two  Eyes. — The  axis  of  the  eye 
is  a  line  passing  through  the  center  of  the  pupil  and  the 
sensitive  spot.  When  we  look  at  anything,  the  axes  of  the 
two  eyes  converge  upon  it  and  it  is  seen  as  a  single  object. 
Two  images  are  formed,  but  they  impress  corresponding 
points  of  the  two  retinae,  and  hence  the  notion  of  a  single 
object  is  conveyed. 


348  LIGHT. 

Fix  the  eyes  on  a  door-knob,  or  any  small  object,  and 
gently  push  one  eyeball  aside  with  the  finger.  The  images 
are  thus  made  to  fall  on  non-corresponding  points  of  the 
retinae,  and  the  object  is  seen  double. 

The  Visual  Angle,  bounded  by  two  lines  drawn  from 
the  eye  to  the  extremities  of  any  object,  measures  the  ap- 

parent size  of  that  object. 
Thus,  the  apparent  sizes  of 
the  sun  and  moon  are  about 
the  same,  although  the  radius 
of  the  sun  is  nearly  twice  the 
distance  from  the  center  of 

FIG.  228.—  THE  VISUAL  ANGLB. 

the  earth  to  the  moon.     In 

Fig.  228,  the  visual  angle  of  the  arrow  B  A  is  I  E  a,  and 
that  of  the  arrow  C  D  is  c  E  d. 

A  given  object  looks  large  or  small  according  to  the  visual  angle 
under  which  it  is  seen.  If  we  measure  the  apparent  lengths  of  the 
equal  arrows  by  an  interposed  rod,  the  nearer  one  will  measure  a  I, 
and  the  farther  one  about  half  as  much,  c  d. 

,  The  visual  angle  of  the  sun  is  nearly  the  same  as  that  of  a  nickel 
five-cent  piece  held  about  seven  feet  away. 


When  the  visual  angle  is  less  than  -g-J-g-  of  a  degree,  or  12 
seconds,  an  object  becomes  invisible. 

Estimation  of  the  Real  Magnitude  and  Distance 
of  Bodies.  —  A  person  born  blind  and  obtaining  his  sight 
after  having  been  educated  as  a  blind  man,  can  not  recog- 
nize bodies  by  the  newly  acquired  sense,  but  continues  to 
do  so  by  touch.  He  handles  objects  again  and  again,  and 
memorizes  their  names  in  connection  with  their  colors  and 
forms,  knowledge  of  colors  being  all  that  the  eye  primarily 
gives.  Everything  appears  to  him  as  if  painted  on  a  screen, 
so  that  notions  of  distance  and  magnitude  have  to  be  ac- 
quired by  slow  experience,  as  in  the  case  of  every  child. 

When  strange  objects  confront  us,  they  are  generally  near  familiar 
things  and  on  familiar  ground,  and  we  at  once  estimate  their  size  by 


INVERSION  OF  THE  IMAGE. 


349 


comparison ;  but  when  we  are  placed  amid  unfamiliar  surroundings, 
we  make  ludicrous  mistakes.  In  a  wild,  mountainous  country,  we  are 
likely  to  mistake  a  mountain  covered  with  enormous  trees,  twenty 
miles  away,  for  a  hill  grown  with  bushes  within  two  miles.  In  such 
a  landscape,  the  presence  of  a  man  or  a  house  at  once  enables  us  to 
form  more  correct  estimates. 

We  can  judge  of  the  distance  of  a  familiar  object  by  its  apparent 
size,  and  we  can  estimate  the  size  of  an  unfamiliar  object  on  familiar 
ground  ;  but  where  real  magnitudes  and  distances  are  unknown,  the 
apparent  size  affords  no  information  regarding  either.  Hence,  on  the 
top  of  Mount  Washington,  or  in  the  parks  of  Colorado,  a  visitor  from 
the  seaboard  is  often  deceived  by  the  apparent  nearness  of  distant  ob- 
jects in  the  clear  and  rarefied  air. 

Why  we  see  Objects  Erect. — The  image  on  the  retina 
is  inverted,  and  yet  we  see  and  localize  objects  as  they  are. 
The  reason  of  this  is  -that  we  do  not  see  the  retinal  image  in 
the  same  sense  that  we  see  external  things.  In  fact,  the 
mere  image  on  the  retina  affords  no  information  to  one  who 
has  not  been  trained  to  interpret  its  meaning  by  touch. 

Engineers  who  use  a  telescope  in  which  everything  is  seen  inverted, 
soon  learn  to  look  through  the  telescope  at  the  rodman  and  direct  his 
movements  without  noticing  that  they  see  him  inverted,  and  that  they 
direct  him  to  move  in  an  opposite  direction  from  that  which  is  appar- 
ently right.  When  thus  trained,  an  engineer,  using  a  telescope  in 
which  everything  is  seen  erect  in  its 
real  position,  would  continually  make 
mistakes.  While  using  such  instru- 
ments alternately,  an  observer  is  fre- 
quently compelled  to  make  a  deliberate 
examination  to  determine  whether  the 
image  in  the  field  is  erect  or  inverted. 

Optical    Imperfections     of 
the    Eye. — Astigmatism. — The 

eye  has  many  defects  common  to 

Other   Optical    instruments.        The  FIG.  229.-TO  ILLUSTRATE 

horizontal  and  the  vertical  curva-  ASTIGMATISM. 

tu re  of  the  ball  are  different,  so  that  when  vertical  lines  are 

in  focus,  horizontal  lines  are  out  of  focus. 


350 

Fig.  229  is  a  diagram  used  for  proving  this  error.  When  held  at  a 
distance,  the  vertical  sectors  are  often  sharply  defined,  while  the  hori- 
zontal ones  are  blurred  and  indistinct.  This  fault  exists  to  some  extent 
ia  all  eyes.  When  very  marked,  it  is  called  Astigmatism  (implying  that 
the  rays  do  not  converge  to  a  point).  Astigmatism  is  corrected  by 
means  of  spectacles  of  cylindrical  curvature,  either  convex  or  concave. 

Irradiation. — A  luminous  body  looks  larger  than  a 
dark  one  of  the  same  size  and  shape.  A  red-hot  wire  and 
the  hot  carbon  filament  of  an  incandescent  lamp  appear 
very  much  larger  than  when  cold,  although  the  real  change 

in  dimensions  by  expansion 

HPHHJ  ^^^        is  wholly  inappreciable. 

^K       ^^  Look  at  a  clean  copper  wire 

H        :     •    and  then  at  a  dull  one  of  the 

K  ^B         ll     '""' ^f    same  caliber.     Hold  a  black  wire 

^^^^^^^^^  ^^^^^^       against  the  sky,  and  then  against 

•HlH^IHH  a  piece  of  white  paper.    What  do 

FIG.  230.— ILLUSTRATING  IRRADIATION.       you  notice  in  each  case  ?   Glance 

at  Fig.   230.     The  white  circle 

surrounded  by  black  looks  larger  than  the  black  circle  surrounded  by 
white,  although  both  are  exactly  the  same  size. 

These  experiments  show  that,  in  bright  images,  the  ret- 
inal effects  extend  beyond  the  geometrical  boundaries  of 
the  images.  The  same  results  are  noticeable  in  photogra- 
phy, and  the  effect  of  complementary  colors  upon  each 
other  is  similar.  It  is  in  accordance  with  this  principle  of 
irradiation,  or  apparent  enlargement  of  brilliant  objects, 
that  persons  of  taste  adapt  the  color  of  their  clothing  to 
their  size  and  figure. 

The  effect  of  contrast  is  always  to  exaggerate.  Small  persons 
seem  diminished  in  size  when  in  the  company  of  those  who  are  taller, 
and  vice  versa. 

Long  and  Short  Sight. — Some  eyes  are  elongated 
along  the  axis,  so  that  the  image  is  formed  in  front  of  the 
retina  unless  the  object  is  held  very  near.  Such  eyes  are 
said  to  be  near-sighted.  They  are  corrected  by  using  di- 
verging glasses. 


LONG  AND  SHORT  SIGHT. 


351 


FIG.  231.— NORMAL,  SHORT-SIGHTED,  AND 
LONG-SIGHTED  EYE. 


Other  eyes  form  the  image  back  of  the  retina  unless  the 
object  is  held  off  at  an  inconvenient  distance,  in  which  case 
it  often  becomes  indistinct.  The  correction  is  here  made 
by  convex  glasses,  as  in 
persons  of  advanced 
years,  who  usually  be- 
come far-sighted. 

In  Fig.  231,  the  normal 
eye,  and  the  rays  a  and  a1 
coming  to  a  focus  on  the 
retina,  are  represented  by 

heavy  lines.  In  the  short-sighted  eye,  where  the  axis  is  too  long,  a 
dotted  line  marks  the  contour ;  an  indistinct  image  is  formed  at  B, 
beyond  the  focus.  The  far-sighted  eye,  with  too  short  an  axis,  is  indi- 
cated in  the  diagram  by  the  hair  line. 

Other  defects  in  the  eye  are  noticed  only  by  those  who  engage  in 
unusual  work.  In  many  optical  researches,  where  divergent  light  en- 
ters the  eye,  the  field  is  seen  full  of  fugitive  shadows  cast  by  particles 
floating  in  the  liquids  of  the  eye.  They  can  usually  be  seen  to  a  lim- 
ited extent  when  one  lies  upon  the  back  and  looks  at  the  sky,  for  when 
the  body  is  erect  they  rise  to  the  upper  part  of  the  ball,  out  of  the 
line  of  vision. 

Chromatic  Aberration  is  another  fault  which  the  eye 
has  in  common  with  all  lenses.  Since  violet  light  is  more 
refracted  than  red  light,  the  principal  focus  for  violet  rays 

will  be  nearer  the  lens  than  that 
for  red  rays.  The  foci  for  all 
other  colors  will  lie  between. 


The  average  eye  when  looking  at 

a  distant  object  is  focused  for  red  rays. 

The  retina  is  at  R.    Violet  will  be 

focused  in  front  of  the  retina,  and  will 

Look  at  a  distant  gas-jet  through  a 


v 
FIG.  232.— CHROMATIC  ABERRATION. 


diverge  into  a  circle  upon  it. 


piece  of  blue  glass.  The  glass  will  cut  off  yellow  and  green  light, 
admitting  blue  and  some  red.  You  will  see  the  flame  red,  surrounded 
by  a  blue  halo.  If  you  now  use  concave  spectacles  of  proper  curva- 
ture, you  will  throw  the  blue  focus  back  upon  the  retina ;  the  red  focus 
will  then  be  behind  the  retina,  and  you  will  see  a  blue  flame  sur- 
rounded by  a  red  halo. 


352  LIGHT. 

The  Blind  Spot. — The  spot  where  the  optic  nerve  en- 
ters the  eye,  is  blind.  To  prove  this,  close  the  right  eye, 
and,  holding  the  book  about  six  inches  from  the  face,  look 
with  the  left  at  the  dot  below.  If  properly  adjusted,  the 


cross  will  be  invisible.  Move  the  book  nearer  to,  or  farther 
from,  the  eye,  and  it  will  reappear.  A  large  dot  and  cross 
may  be  placed  on  the  blackboard,  the  size  being  greater  in 
proportion  to  the  distance.  When  the  cross  disappears,  on 
approaching  or  receding,  its  image  falls  on  the  blind  spot.  If 
the  left  eye  is  closed,  the  right  must  be  directed  to  the  cross. 

The  image  of  a  lamp-globe  or  the  full  moon  may  be  shut  out  in 
this  manner.  The  blind  spot  is  large  enough  to  cause  the  disappear- 
ance of  seven  full  moons  placed  side  by  side. 

The  experiments  described  above  prove  that  the  optic  nerve  is 
blind,  and  that  the  true  function  of  the  retina  is  the  mysterious  con- 
version of  vibrations  of  ether  into  the  proper  excitants  of  this  nerve, 
whose  fibers  communicate  to  the  brain  sensations  of  light  and  color. 

Care  of  the  Eye. — The  eye  is  admirably  adapted  to  the 
wants  of  a  pastoral  or  savage  people,  not  even  failing  them 
in  old  age  ;  but  the  increasing  demands  of  a  civilized  life 
bring  it  into  use  under  conditions  which  it  is  not  so  com- 
pletely designed  to  satisfy.  Injury  to  the  eye  may  be  pre- 
vented and  its  usefulness  prolonged  by  observing  the  fol- 
lowing precautions  : — 

Do  not  use  the  Eyes— 1.  In  insufficient  light,  as  in  deepen- 
ing twilight,  or  when  the  sun  is  obscured  by  a  rain-cloud.  2.  In  ex- 
cessive light,  as  the  glare  of  the  sun  or  of  an  electric  arc.  3.  In  un- 
steady light,  as  that  of  a  flickering  gas-jet — the  effect  of  persistent 
reading  in  a  moving  carriage  or  railway-train  is  in  the  end  equally 
pernicious.  4.  In  hot  light,  as  that  of  powerful  kerosene  burners, 
which  over-congests  the  retina.  5.  Do  not  sleep  with  a  light  in  the 
room,  as  the  eyelids  are  semi-transparent,  and  both  retina  and  brain, 
which  should  have  rest,  are  continuously  irritated.  6.  Avoid  sudden 
and  intense  changes  of  light,  as  the  pupil  responds  slowly.  7.  Avoid 
light  that  enters  the  eye  directly.  While  working,  use  an  opaque 


THE  STEREOPTICON.  353 

lamp-shade.     The  artificial  light  that  most  nearly  fulfills  the  con- 
ditions of  a  perfect  illuminator  is  the  German  student's  lamp. 

QUESTIONS.— Prove  that  the  human  eye  is  practically  a  camera.  Describe  mi- 
nutely its  anatomy  ;  its  several  coats,  its  lens,  its  humors,  the  office  of  the  iris. 
How  can  you  prove  there  is  a  spot  of  distinct  vision  ?  How  is  the  eye  accom- 
modated to  objects  of  varying  distance  ?  Explain  the  principle  of  single  vision 
with  two  eyes  ;  of  the  determination  of  size  and  distance.  On  what  does  ap- 
parent magnitude  depend  ?  Why  do  the  sun  and  the  moon  appear  larger  when 
near  the  horizon  ?  How  long  is  a  child  in  acquiring  an  approximately  correct 
appreciation  of  distance  and  magnitude  ?  About  three  years.  Why  do  we  see 
objects  erect  ? 

What  is  astigmatism  ?  Illustrate  irradiation.  Explain  long  and  short  sight. 
When  an  image  is  formed  in  the  vitreous  humor  instead  of  on  the  retina,  what 
kind  of  glasses  are  required  ?  Why  do  old  persons  hold  objects  at  a  distance 
in  order  to  see  them  distinctly  ?  What  kind  of  eyes  require  double  convex 
spectacles  ?  Can  you  give  a  reason  for  not  forming  the  habit  of  reading  while 
lying  on  the  back  ?  Explain  chromatic  aberration  in  the  eye. 

What  is  the  blind  spot  ?  Describe  experiments  that  prove  its  existence.  State 
precisely  the  office  of  the  optic  nerve  and  of  the  retina.  What  precautions 
should  be  observed  by  persons  desirous  of  preserving  their  eye-sight  ?  Why 
does  a  sudden  entrance  into  bright  light  give  pain  to  the  eye  for  a  time  ?  Why 
is  it  injurious  to  the  eye  to  sleep  with  a  lighted  lamp  in  the  room  ?  Is  it  true 
that  cats  and  owls  can  see  in  the  entire  absence  of  light  ?  Will  a  diamond 
glisten  or  a  cat's  eyes  shine  in  the  dark  ?  Why  is  the  pupil  of  every  eye  black  ? 


OPTICAL  INSTRUMENTS  THAT  AID  VISION. 

The  Stereopticon,  the  converse  of  the  camera,  is  used 
for  throwing  magnified  images  on  a  screen  in  a  darkened 
room.  A  transparency 
or  slide,  produced  by 
the  camera,  is  placed 
at  S  and  powerfully 
illuminated  by  an  elec- 
tric or  lime  light  L, 
the  latter  produced  by 

the    combustion   of  a      ^  ,A_Vmm  OF  THE  STEREOPTICOK. 
lime-stick  with  the  aid 

of  oxygen  and  hydrogen  gas  under  pressure  in  the  cylinders 
0  and  H.  The  condensing  lenses,  X,  serve  to  converge  the 
rays  upon  it,  and  a  focusing  lens,  D,  produces  a  real,  in- 
verted, and  enlarged  image  I  upon  a  screen  (see  Fig.  233). 


354 


LIGHT. 


The  position  of  the  focusing  lens  D  can  be  varied  so  as  to  bring 
the  image  on  the  screen.  The  farther  the  screen  is  away,  the  nearer 
the  lens  must  be  moved  up  toward  the  slide.  If  the  slide  be  brought 
up  to  the  principal  focus,  the  image  will  be  infinitely  distant. 

In  the  camera,  the  picture  of  the  external  object  is  formed  on  the 
slide.  In  the  stereopticon,  the  slide  is  used  to  reproduce  a  representa- 
tion of  the  original  object.  The  image  in  the  one  instrument  corre- 
sponds to  the  object  in  the  other. 

The  simplest  form  of  the  stereopti- 
con is  the  ordinary  magic  lantern,  which 
the  pupil  may  easily  construct  as  follows : 
Make  a  tube  for  the  focusing  lens  by 
winding  paper  round  a  broomstick  or 
curtain -pole  of  the  required  diameter, 
applying  mucilage  at  every  turn.  Set  this 
when  dry  in  a  cigar-box  furnished  with  a 
tin  chimney.  Use  a  common  burning- 
glass  for  the  condenser,  with  a  tin  reflector 
behind  it  and  a  kerosene-lamp  for  illumi- 
nation. If  photography  is  an.accomplish- 
ment  of  the  pupil,  he  can  supply  original 
illustrations  for  his  magic  lantern  with- 
out limit  should  he  further  master  the 
process  of  printing  positive  transparencies 
from  his  glass  negatives.  (Precise  in- 
structions for  making 
simple  slides  are  given  in 
Mayer  and  Barnard's 
"  Light,"  pages  87-89.) 

The  Compound 
Microscope  is  an  in- 
strument designed  to 
produce  magnified 
images  of  objects  too 
small  to  be  seen  with 
the  naked  eye.  In 
Fig.  235  the  object  a 
is  placed  just  outside  the  principal  focus  of  a  lens  or  combi- 
nation of  lenses,  0,  and  a  real  magnified  and  inverted  image, 
b  c,  is  formed.  This  image  is  then  itself  magnified  at  B  C 


FIG.  234.— COMPOUND 
MICROSCOPE. 


FIG.  235.— DIAGRAM  ILLUS- 
TRATING ACTION  OF  THE 
COMPOUND  MICROSCOPE. 


THE  TELESCOPE.  355 

by  means  of  a  simple  microscope  E,  called  the  eye-lens.  The 
latter  is  usually  mounted  in  a  sliding  tube,  so  that  it  can  be 
properly  placed  with  respect  to  the  image.  The  lens  and 
tube  together  constitute  the  eye-piece.  If  the  magnifying 
power  of  0  is  fifty,  and  that  of  E  four,  the  image  seen  will 
be  two  hundred  times  the  size  of  life. 

Chromatic  aberration  in  the  microscope  is  corrected  by  using  a 
concave  lens  in  combination  with  the  object-lens  0. 

As  in  the  case  of  the  photo-micrographic  camera,  the  microscope 
may  be  combined  with  the  stereopticon,  and  illustrations  of  minute 
objects  thrown  upon  a  screen  for  the  instruction  of  an  audience.  The 
electric  light  is  now  generally  used  for  illumination,  and  the  instru- 
ment is  therefore  known  as  the  photo-electric  microscope. 

Astronomical  Telescope. — The  telescope  produces  a 
magnified  image  of-  an  object  which  appears  small  because 
it  is  far  away.  The  instrument  consists  of  an  object-glass 
0  (Fig.  236),  which  forms  a  real,  inverted,  and  diminished 


0  l^"    E 

D 
FIG.  236.— DIAGRAM  ILLUSTRATING  PRINCIPLE  OF  ASTRONOMICAL  TELESCOPE. 

image,  a  #,  of  the  distant  object  A  B.  This  image  is  viewed 
by  means  of  a  simple  microscope  E,  as  in  the  case  of  the 
compound  microscope,  and  is  thus  magnified  at  C  D. 

In  the  terrestrial  telescope,  or  field-glass,  two  additional  lenses  are 
introduced  between  the  real  image  and  the  eye-lens,  with  the  effect  of 
correcting  the  inversion  and  showing  the  object  in  its  natural  position. 

The  telescope  at  Lick  Observatory  on  Mount  Hamilton,  California 
(4,200  feet  above  sea-level),  is  the  largest  and  most  powerful  in  the 

NOTE.— A  serviceable  compound  microscope  may  be  obtained  of  Messrs. 
Queen  &  Co.  at  the  extremely  moderate  price  of  five  dollars.  Provided  with  two 
object-lenses,  which,  in  connection  with  the  eye-piece,  magnify  several  thousand 
times,  it  is  capable  of  affording  endless  entertainment  to  the  young  investigator 
interested  in  the  study  of  animal  and  plant  life.  Much  may  be  learned  from 
the  use  of  a  pocket  magnifier,  which  is  a  simple  microscope. 


FIG.  237.— THE  LICK  TELESCOPE. 

Length,  57  feet ;  diameter  of  object-glass,  36  inches ;  total  weight,  40  tons ; 
magnifying  power,  180  to  3,000  diameters. 


TELESCOPE  AND  MICROSCOPE. 


35T 


world.  The  tube  is  fifty-seven  feet  in  length,  or  nearly  as  long  as  the 
shaft  of  the  New  York  obelisk.  The  two  glasses  which  form  the  ob- 
jective (a  yard  in  diameter)  cost  over  $50,000. 

The  telescope  is  driven  by  a  clock  inside  the  pier,  which  causes  it 
to  move  so  as  to  follow  any  star  upon  which  it  is  directed.  The  rods 
seen  along  the  tube  are  intended  to  clamp  the  telescope  on  its  axes, 
and  to  move  it  when  it  is  not  quite  in  position.  The  circles  are  also 
read  by  means  of  long  microscopes.  All  these  fittings  are  thus  ac- 
cessible to  the  observer  when  standing  at  the  eye-lens. 

The  Relation  between  Microscope  and  Telescope 

may  be  impressively  illustrated  by  the  pupil  with  the  fol- 
lowing simple  apparatus : 

In  Fig.  238,  S  represents  a  screen  of  cardboard,  through  which  a 
cross,  with  arms  about  half  an  inch  long,  has  been  cut.  This  cross  is 
illuminated  by  a  gas-jet  L.  0  is  a  lens  (a  large  pocket-lens  will  an- 
swer) which  is  placed  eight  or  ten  feet  from  S,  and  produces  an 


s; 


FIG.  238. — ILLUSTRATING  THE  RELATION  BETWEEN  MICROSCOPE  AND  TELESCOPE. 

image  of  the  luminous  cross  upon  a  screen  S'.  Mark  the  dimen- 
sions of  the  image  in  pencil,  and  cut  it  through  the  card.  E  is  a  lens 
so  placed  that  the  card  S'  is  distinctly  seen  through  it.  Now  remove 
S'  and  look  through  the  two  lenses  at  the  card  S.  This  arrangement 
constitutes  a  telescope. 

Next  let  the  flame  and  the  eye-lens  E  change  places.  Focus  the 
eye-lens  on  S.  The  image  of  the  luminous  cross  in  S'  is  now  repre- 
sented by  the  cross  in  S.  Remove  S  and  look  at  the  screen  S'.  This 
arrangement  is  a  microscope. 

The  focal  length  of  the  objective  of  a  microscope  is  usually  very 
short  compared  with  that  of  the  telescope  objective. 

Magnifying  Power. — As  seen  through  the  telescope  or 
microscope,  an  object  appears  a  certain  number  of  times  as 
large  as  when  seen  from  the  same  point  with  the  unaided 


358 


LIGHT. 


eye.  This  number  is  called  the  magnifying  power  of  the 
instrument.  In  Fig.  239,  c  d  represents  the  image  of  the 
object  A  B.  If  c  d  is  projected  to  the  same  distance  as  the 
object,  its  length  would  be  c'  d'.  Hence  the  magnifying 

power  in  diameters  is,  in  this  case,  -7-73- 

A  _D 

With  one  eye  look  through  a  telescope  at  a  brick  in  a  wall,  and  at 
the  same  time  observe  the  wall  itself  with  the  other.  The  image  of 

the  brick  seen  through  the  tele- 
scope may  appear  as  wide  as  ten 
bricks  viewed  with  the  unaided 
eye.  Suppose  A  B  to  be  a  card 
pinned  against  a  wall.  An  assist- 
ant may  then  mark  the  points  c' 
and  d  with  a  pencil,  as  directed 
by  the  observer  at  the  telescope. 
A  B  and  c'  d  are  then  measured 
by  a  foot-rule.  The  ratio  of  these  two  lengths  is  the  magnifying  power. 

The  Stereoscope. — The  views  used  in  the  common 
stereoscope  are  photographs  taken  from  slightly  different 
positions.  The  view  on  the  left  side  of  the  card  represents 


C1"' 


FIG.  239. — MAGNIFYING  POWER. 


FIG.  240. — PRINCIPLE  OF  THE  STEREOSCOPE  ILLUSTRATED. 

the  object  as  seen  by  the  left  eye,  while  the  other  view  rep- 
resents it  as  seen  by  the  right  eye.  Fig.  240  illustrates  two 
such  views  of  a  pyramid. 


THE  STEREOSCOPE.  359 

If  these  figures  are  observed,  with  the  eyes  focused  on  a  distant 
object,  each  one  will  be  seen  double.  The  two  inside  images  can  be 
superposed,  and  will  then  appear  in  relief  like  a  solid  standing  up  from 
the  paper.  This  effect  is  more  easily  realized  by  holding  a  card  or 
paper  between  the  eyes  and  between  the  two  pictures,  so  that  the  right 
eye  can  see  only  the  right  picture,  and  the  left  eye  the  left  picture. 

The  stereoscope  is  designed  to  aid  in  the  combination 
of  these  pictures,  giving  to  the  result  a  solid 
appearance. 

The  two  pictures  are  represented  by  P 
and  P'  in  Fig.  241.  The  diaphragm  or  par- 
tition D  prevents  the  right  eye  from  seeing 
the  left  picture,  and  vice  versa.  The  half 
lenses  L  and  L'  refract  the  light  coming  from 

ijfe*    ^  <M-    the  pictures  P  and  P',  so  that  it  seems  to 

sjf  \     have' come  from  C. 

FIG.  241.-PATH  OP          B    means  of  these  refractors  it  is  possible  to 

RAYS  IN  STEREO-  ...  . .  . 

SCOPE  superpose  pictures  which  would  be  too  large  to  man- 

age with  the  unaided  eyes.  Should  the  two  dia- 
grams shown  in  Fig.  240  be  copied  on  cards,  the  effect  in  the  stereo- 
scope will  be  very  striking.  If  the  two  pictures  exchange  positions, 
how  will  the  combined  image  appear  1? 

QUESTIONS.— Describe  the  Stereopticon.  Compare  it  with  the  camera.  How  may 
a  simple  lantern  be  constructed  ?  What  should  be  used  as  slides  ?  Explain 
the  difference  between  a  simple  and  a  compound  Microscope  ;  between  the 
images  respectively  formed  by  each.  What  is  the  Photo-electric  Microscope  ? 

Describe  the  Astronomical  Telescope  and  the  image  formed  in  the  tube.  What  is 
the  character  of  the  image  in  the  ordinary  spy-glass  ?  How  is  the  change  ef- 
fected ?  What  can  you  say  of  the  telescope  at  Lick  Observatory  ?  Illustrate 
the  relation  between  microscope  and  telescope.  How  is  the  magnifying  power 
of  an  instrument  determined  ?  Explain  the  principle  of  the  Stereoscope. 


PHOTOMETRY  AND  POLARIZATION  OF  LIGHT. 

Photom'etry  (light -measuring). — As  thermometers  are 
used  for  measuring  heat,  so  there  are  instruments  by  which 
the  intensity  of  light  may  be  estimated. 

The  standard,  in  the  case  of  light,  is  the  flame  of  an 
English  sperm-candle  burning  120  grains  an  hour.  Other 


360 


LIGHT. 


sources  of  light  may  be  compared  with  a  sperm-candle  by 
means  of  a  photom'eter. 

The  Bunsen  photometer  is  shown  in  Fig.  242.    It  consists  of  a 
screen  of  paper  S,  mounted  in  a  box  B,  which  slides  to  and  fro  on  a 


FIQ.  242.— THE  BUNSEN  PHOTOMETER. 

graduated  bar.  The  paper  screen  has  a  central  spot  saturated  with 
paraffine.  One  side  of  the  screen  may  be  illuminated  by  two  standard 
candles,  and  the  other  side  by  a  gas-flame  or  electric  lamp.  When  the 
screen  is  so  placed  that  the  two  sides  are  equally  illuminated,  the  par- 
affine spot  is  invisible.  When  one  side  is  more  strongly  illuminated, 
the  spot  appears  dark  on  that  side  and  light  on  the  other. 

If  a  standard  candle  is  lighted  at  each  end,  the  screen  must  be 
placed  midway  of  the  bar  to  render  the  paraffine  disk  invisible.  If  4 
or  9  candles  are  placed  at  L'  and  one  at  L,  the  distance  L'  B  must  be 
two  or  three  times  the  distance  L  B  to  insure  the  same  effect.  The 
candle-power  of  the  two  lights  is  directly  proportional  to  the  square  of 
the  distances  from  the  screen.  The  photometer  should  be  used  in  a 
dark  room  having  blackened  walls.  The  room  may  be  made  of  heavy 
paper  tacked  on  a  frame.  The  sliding  box  may  easily  be  extemporized 
from  a  cigar-box,  but  the  paraffine  disk  and  sperm-candles  should  be 
ordered  of  a  dealer  in  physical  instruments. 

The  bar  is  usually  100  inches  long  and  may  be  graduated  to  inches. 
These  bars  are  generally  graduated  in  candle-power  direct.  If  the  disk 
stands  at  64  when  the  illumination  is  equal, 

(64\2 
•ggvj  times  as 

strong  as  the  other,  the  stronger  light  being 
the  one  farthest  from  the  disk. 

In  order  that  both  sides  of  the  disk  may  be 
seen  at  once,  two  strips  of  mirror,  m'  and  m" 
(Fig.  243),  are  placed  in  a  vertical  position  in 
the  back  of  the  box,  so  that  the  eyes  at  E'  and 
E"  will  see  the  two  images  of  the  luminous  spot  S  at  S'  and  S". 


POLARIZATION  OF  LIGHT. 


361 


In  precise  work,  it  is  customary  to  weigh  the  candles  be- 
fore and  after  the  test,  for  the  purpose  of  determining  the 
amount  of  sperm  burned  in  a  given  time.  Two  candles 
should  lose  40  grains  in  10  minutes.  If  they  lose  39,  the 
two  candles  are  f-§-  of  two  standard  candles. 

If  the  disk  stands  on  the  average  80  inches  from  the  electric  lamp 
or  20  from  the  candles,  while  the  two  candles  burn  39  grains  of  sperm 
in  10  minutes,  the  candle-power  of  the  lamp  would  be — 

/80\*     39 

(iff)   X40X3- 

Polarization  by  Reflection. — If  the  direct  light  of 
the  sun  be  received  upon  a  plate  of  polished  black  glass,  it 
can  be  reflected  in  any  direction  upon  the  walls  of  a  room. 
The  character  of  light  thus  reflected  is  radically  changed. 


FIG.  244.  FIG.  245. 

POLARIZATION  BY  REFLECTION. 

The  properties  of  the  reflected  ray  are  not  now  symmetrical 
around  the  ray.     There  are  certain  directions  in  which  it 
can  not  again  be  reflected. 
24 


862  LIGHT. 

In  Fig.  244,  light  is  represented  striking  the  lower  mirror,  and  re- 
flected upon  a  second  mirror  above.  The  mirrors  admit  of  being 
turned  on  their  horizontal  axes.  So  long  as  these  axes  are  parallel, 
light  will  be  reflected,  as  shown  in  Fig.  244. 

Turn  the  upper  mirror  around  a  vertical  axis  through  an  angle  of 
90°,  so  that  the  axes  upon  which  the  mirrors  are  mounted  are  crossed, 
as  shown  in  Fig.  245.  When  the  two  mirrors  are  set  so  that  the  light 
on  each  is  incident  at  an  angle  of  54°  35',  no  light  will  be  reflected 
from  the  second  mirror ;  a  black  spot  will  appear  in  the  center  of  the 
field  of  view.  If  the  mirrors  be  kept  at  this  angle,  and  the  upper  one 
revolved  about  a  vertical  axis,  the  light  will  grow  stronger  until  the 
mirror  has  turned  90°.  Then  it  begins  to  grow  feebler  until  the  mir- 
ror has  turned  another  90°,  when  it  is  again  wholly  extinguished. 

Light  which  behaves  in  this  manner  is  said  to  be  plane 


According  to  the  accepted  undulatory  theory  of  light, 
an  ordinary  ray  contains  vibrations  in  many  planes ;  but  a 
polarized  ray  vibrates  in  a  single  plane.  The  unaided  eye 
fails  to  distinguish  between  them.  In  the  apparatus  just 
described,  the  lower  mirror  is  called  the  polarizer,  the  upper 
the  analyzer ;  the  former  produces  polarization,  the  latter 
makes  it  evident. 

Light  is  also  polarized  by  reflection  from  water.  From  the  amal- 
gam of  an  ordinary  mirror  the  reflected  beam  acts  like  the  direct  sun- 
beam, as  far  as  reflection  from  a  glass  plate  is  concerned.  It  has, 
however,  been  affected  in  a  manner  that  the  student  may  study  in 
more  advanced  works,  under  the  head  of  circular  polarization.  Re- 
flected light  from  some  bodies,  like  the  metals,  can  not  be  wholly 
quenched  by  a  second  reflection  from  glass.  The  brightness  of  the 
beam  passes  through  a  minimum,  instead  of  becoming  zero. 

Polarization  by  Double  Refraction. — If  a  strong 
beam  of  light  be  directed  through  a  slit  in  a  cardboard,  in 
front  of  which  is  a  focusing  lens,  an  image  of  the  slit  will  be 
projected  upon  the  screen  (see  Fig.  246).  Interpose  a  pol- 
ished rhombohedron  of  calcite  (Iceland-spar)  between  the 
slit  and  lens.  Two  images  of  the  slit  will  at  once  appear. 
By  looking  into  the  face  from  which  the  light  emerges,  it 


DOUBLE  REFRACTION. 


363 


will  be  observed  that  the  beam  has  separated  into  two  beams 
of  light,  each  of  which  gives  an  image  of  the  slit.  That 
these  beams  separate,  is  clearly  evidence  that 
one  of  them  has  been  refracted  more  than  the 
other. 


FIG.  246.— ILLUSTRATING  POLARIZATION  BY  DOUBLE  REFRACTION. 

By  reflecting  these  beams  from  a  mirror  of  black  glass,  it  will  be 
found  that  they  are  polarized  at  right  angles  to  each  other.  If  the 
mirror  is  placed  at  the  proper  angle,  one  of  these  rays  will  be  reflected 
at  its  maximum  of  brightness,  and  the  other  will  be  extinguished  at 
the  mirror.  Turn  the  mirror  90°  around  the  rays  as  an  axis ;  the  ray 
which  had  been  extinguished  will  now  be  reflected,  and  vice  versa. 
For  intermediate  positions,  both  images  of  the  slit  will  be  seen  upon 
the  walls  of  the  room,  and  for  the  middle  position  they  will  be  of  equal 
brightness. 

The  distinct  paths 
taken  by  rays  of  light  in 
their  passage  through 
Iceland -spar  may  be 
more  simply  illustrated 
by  placing  a  crystal  of 
the  mineral  over  a  piece 
of  paper  containing  let- 
ters. Each  letter  will 
appear  double;  but  if 
the  crystal  be  revolved, 

one  set  of  letters  will  revolve  round  the  other.  This  is  more  clearly 
shown  if  a  black  dot  be  used  as  an  object.  Other  substances  doubly 
refract,  notably  ice. 

The  NicoPs,  or  Single-Image,  Prism  is  a  simple  con- 
trivance for  polarizing  light.    It  consists  of  a  rhombohedron 


FIG.  247.— PHENOMENON  OF  DOUBLE  REFRACTION. 


364 


LIGHT. 


of  calcite,  which  has  been  sawed  through  from  one  obtuse 
angle  to  the  opposite,  as  along  the  diagonal  plane  a  c  b  d,  in 
Fig.  248.  These  surfaces,  being  polished,  are  cemented  to- 
gether with  Canada  balsam.  The  ray  of  common  light  S  I, 
on  entering  the  prism,  is  refracted  into  two  rays.  One 
strikes  the  balsam  surface  at  an  angle  greater  than  the  criti- 
cal angle,  and  is  reflected  out  of  the  side  of  the  crystal  as 
o  0.  The  instrument  thus  furnishes  a  single  beam  of  plane 
polarized  light  e  E.  It  is  more  generally  used  than  a  mir- 

ror  of  black  glass,  as  the  ray  can 
be  kept  in  the  same  line  through 
two  successive  Nicol's  prisms. 

If  the  transmitted  beam  is  sent 
through  a  second  prism  in  a  similar 
position,  it  will  be  again  transmitted. 
Turning  either  prism  through  90°  ren- 
ders the  field  dark.  The  second  prism 
will  cut  off  the  light  which  the  first 
transmitted. 

Place  a  common  window-glass  over 
a  printed  page,  in  front  of  a  window, 
and  step  back  until  the  light  reflected 
from  the  glass  prevents  you  from  see- 
ing the  print  below.  This  light  is 
polarized,  and  will  be  extinguished  by 
a  crossed  Nicol.  The  print  will  then 
become  visible.  In  the  same  way  the 

light  reflected  from  water  may  be  cut  off,  so  that  objects  below  the 

surface  can  be  distinctly  seen. 

Observe  reflections  from  various  objects  through  a  Nicol's  prism, 

turning  the  instrument  to  determine  the  positions  of  maximum  and 

minimum  brightness.     Observe  the  sky  in  a  similar  manner. 

Beautiful  colors  are  produced  by  the  action  of  polarized 
light.  If  a  thin  plate  of  mica  or  sel'enite  (moonstone)  be 
placed  between  the  polarizer  and  the  analyzer,  the  field  will 
be  tinted,  the  color  depending  on  the  thickness  of  the  plate. 
A  section  of  calcite  cut  perpendicular  to  the  axis  of  the 
crystal,  when  viewed  by  divergent  polarized  light,  exhibits 


FIG.  248.— NICOL'S  PRISM. 


THE   POLAKISCOPE. 


365 


brilliant  colored  rings  with  a  cross  which  is  black  or  white, 
according  to  the  position  of  the  analyzer.  These  rings  may 
be  seen  with  the  tourmaline  polariscope,  p.  366. 

A  cheap  analyzer  may  be  made  from  a  bundle  of  thin  microscope 
glass.    Six  or  eight  slides  superposed  and  mounted  in  any  convenient 
way  will    serve    very 
well.  Observe  oblique- 
ly through  the  bundle. 
The  color  shown   by 
selenite  or  mica  can  be 
seen  if  two  panes  of 
ordinary  window-glass 
are  held  in  the  posi- 
tions   represented    in 
Figs.  244  and  245,  the      FlG  349.— RINGS  AND  CROSS  BY  POLARIZED  LIGHT. 
selenite  or  mica  sheet 

being  interposed  between  them.  All  fine  microscopes  are  now  pro- 
vided with  a  polarizing  set,  consisting  of  two  Nicol's  prisms,  for  the 
delicate  structures  of  many  objects  can  be  studied  only  under  polar- 
ized light. 

A  Polariscope  may  be  improvised  as  follows :  Place  a 
plate  of  black  glass  or  a  piece  of  window-pane,  G,  on  a 
base-board,  which  also  supports  a  Nicol's  prism  at  P  (Fig. 

250).  The  axis  of  the 
Nicol  is  mounted  at  an  an- 
gle of  35°  25'  with  the  sur- 
face of  the  mirror.  A 
support,  S,  serves  for  hold- 
ing transparent  objects 
which  are  to  be  examined 
in  polarized  light.  A  piece 
of  ground  glass,  L,  may  be 
used  to  cut  off  the  images 

of  external  objects.  The  instrument  should  be  placed  in 
front  of  a  window,  and  the  whole  may  be  covered  with  a 
cloth  to  cut  off  light. 

The  Tourmaline  Polariscope. — The  mineral  tour'- 
maline  possesses  in  a  high  degree  the  property  of  polarizing 


FIG.  250.— A  SIMPLE  POLARISCOPE. 


366 


LIGHT. 


light.  Two  tourmaline  plates,  set  in  a  mounting  so  that 
the  plates  can  be  rotated,  will  thus  serve  as  a  polariscope. 
When  the  plates  are  crossed, 
as  shown  in  the  figure,  the  field 
is  dark.  If  we  turn  either 

plate    90°,    we    shall     find     the    FlG-  ^--TOURMALINE  POLAKISCOPE. 

field  to  be  bright,  although  colored  by  the  tourmaline.     The 
plates  are  alike,  and  either  may  be  used  as  an  analyzer. 

Applications  of  Polarized  Light. — The  Saccha- 
rimeter. — The  polarization  of  light  is  used  in  measuring 
the  strength  of  sugar  solutions. 

In  Fig.  252,  m  is  a  polarizing  mirror  which  reflects  abeam  of  polar- 
ized monochromatic  light  through  a  Nicol's  prism,  a,  serving  as  the  an- 
alyzer. The  Nicol  is  so  placed  that  the  field  is  dark.  If  a  tube,  d,  filled 

with  sugar  solution  be 
interposed  between  the 
polarizer  and   analyzer, 
the  field  becomes  bright. 
If  the  Nicol  is  rotated 
through   a  small 
angle,    the    field 
again       becomes 
dark.    This  angle 
is  greater,  the  stronger 
the  sugar  solution.  With 
pure  water  the  angle  is 
zero. 

By  noting  the  angle 
through  which  the  Nicol 
must  be  turned,  the 
strength  of  the  solution 
may  be  determined. 
Solutions  of  known 
strength  are  first  examined  in  order  to  find  the  amount  of  sugar  re- 
quired to  cause  a  rotation  of  1°  for  a  given  tube. 

When  cane-sugar  is  examined,  the  analyzer  must  be  turned  to  the 
right  in  order  to  produce  a  dark  field ;  but,  when  a  solution  of  glucose 
is  examined,  the  rotation  must  be  in  the  opposite  direction.  The  mir- 
ror m  may  be  replaced  by  a  Nicol  polarizer. 


FIG.  252.— THE  SACCHARIMETER. 


THE  RAINBOW.  367 

The  principle  of  polarization  is  further  applied  in  exam- 
ining into  the  nature  of  crystals,  in  difficult  chemical  analy- 
ses, and  in  determining  whether  light  from  the  heavenly 
bodies  is  reflected  from  planets  and  moons,  or  emitted  by 
suns.  The  corona  of  the  sun  has  been  photographed  during 
eclipses  by  light  polarized  in  many  planes,  and  thus  has 
been  proved  to  shine  by  reflected  light. 

QUESTIONS. — What  is  Photometry  ?  Describe  the  Bunsen  photometer.  State 
what  you  understand  by  polarized  light.  Show  how  light  may  be  polarized  by 
reflection.  Can  the  eye  distinguish  between  polarized  and  ordinary  light  ?  In 
a  polarizing  apparatus,  distinguish  the  polarizer  from  the  analyzer. 

Explain  the  phenomenon  of  double  refraction.  Illustrate  with  a  piece  of  Iceland- 
spar.  What  is  a  Nicol's  prism  ?  How  is  it  made  ?  State  how  it  is  used ; 
how  it  may  render  objects  below  the  surface  of  water  visible ;  how  it  may 
produce  colors.  Having  a  Nicol's  prism,  can  you  design  a  polariscope  ?  De- 
scribe the  tourmaline  polariscope.  Explain  some  applications  of  polarized 
light.  How  is  it  of  use  to  the  microscopist  ?  To  the  chemist  ?  To  the  astron- 
omer ? 


APPLICATION  OF  THE  PRINCIPLES  OF  REFRAC- 
TION, REFLECTION,  AND  DISPERSION,  IN 
THE  RAINBOW. 

The  Rainbow  is  produced  by  sunlight  passing  through 
drops  of  water,  which  act  as  prisms.  It  is  composed  of  the 
seven  prismatic  colors.  There  are  sometimes  two  concentric 
bows.  The  inner  or  primary  bow  shows  the  spectrum  colors 
in  regular  order,  the  red  being  outermost.  The  secondary 
bow  shows  the  colors  in  reverse  order,  the  red  being  inner- 
most. The  center  of  the  bows  is  determined  by  a  line 
passing  through  the  center  of  the  sun  and  the  eye  of  the 
observer.  This  line  is  called  the  axis  of  the  bow. 

Conditions  of  Visibility  of  the  Rainbow. — The  ob- 
server must  stand  with  his  back  to  the  sun,  and  the  drops 
which  produce  the  bow  must  be  in  front  of  him. 

If  the  sun  is  in  the  horizon,  half  of  the  complete  circles 
will  be  seen  above  the  horizon. 

In  the  dense  spray  of  Niagara,  the  rainbow  is  seen  as  a  complete 
circle,  and  apparently  only  a  few  feet  distant.  In  an  ordinary  rain-storm, 


368 


LIGHT. 


the  part  of  the  bow  below  the  horizon  is  not  usually  visible  in  a  level 
region,  because  there  is  not  a  sufficient  number  of  drops  between  the 
eye  and  the  immediate  foreground  to  produce  an  appreciable  effect. 

Action  of  the  Bain-drop.  —  In  Fig.  253,  the  circle 
whose  center  is  at  D  represents  a  section  of  a  rain-drop.     A 

ray  of  sunlight,  S  #,  falling  on 
the  upper  part  of  the  drop,  will 
be  in  part  reflected  ;  but  some 
of  the  light  will  enter  the  drop. 
Of  this  light,  incident  upon  the 
inside  of  the  surface  at  n9  part 
will  pass  out  again  into  the  air. 

FIG.  253.—  ACTION  OF  RAIN-DROP  IN    ...,*..,,        .     ,  ,, 

FORMATION  OF  PRIMARY  BOW.      The  rest  being  internally  reflected 
is  again  internally  incident  at  a'. 

Here  the  same  result  follows  as  at  n,  and  the  light  which 
escapes  into  the  air  proceeds  to  the  eye  at  E. 

If  this  drop  is  so  situated  as  to  send  red  light  to  the  eye,  then, 
since  they  are  more  refracted,  violet  and  in  fact  all  other  colors  will  be 
thrown  above  the  eye,  as  in  a!  v, 
representing  the  violet  ray.  The 
drops  which  send  violet  to  the 
eye  at  E  must  therefore  lie  be- 
low those  sending  red. 

In  the  formation  of  the 
secondary  bow,  two  internal 
reflections  take  place,  as 
shown  in  the  drops  D  D 
(Fig.  254). 

Here  the  eye,  E,  is  sup- 
posed to  be  far  above  the 
ground,  G  G.  The  sun's 
rays,  S  and  S',  being  hori- 


zontal, the  sun  is  assumed 

-    '  .  FIG.  254.—  FORMATION  OF  SECONDARY  Bow. 

to  be  in  the  horizon.     Two 

rays,  S,  enter  drops,  the  one  at  the  top  and  the  other  at 

the  bottom  of  the  complete  circular  bow  which  would  be 


PROBLEMS  IN  LIGHT.  369 

visible  at  that  altitude.  They  are  supposed  to  send  violet 
light  to  the  eye  after  one  reflection,  the  rays  being  marked 
v  p.  The  rays  v  s  are  the  violet  rays  of  the  secondary  bow. 
The  drops  are  represented  at  different  distances  from  the  eye. 

If  the  ground  were  at  G'  G',  then  only  half  of  the  bows  would  be 
visible,  unless  the  region  immediately  around  the  eye  were  filled  with 
a  dense  spray,  when  a  complete  circular  rainbow  of  the  same  angular 
magnitude  might  be  seen.  The  real  diameter  of  a  bow  is  indefinite,  as 
some  of  the  drops  producing  it  may  be  only  ten  feet  from  the  eye, 
while  another  drop  an  instant  later,  sending  the  same  color  to  the  same 
part  of  the  retina,  may  be  a  mile  away. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

The  nearest  fixed  star  is  about  25,000,000,000,000  miles  away.  How  long  is  light 
in  coming  from  this  star  to  the  earth  ? 

A  cannon-ball,  maintaining  a  constant  average  velocity,  would  require  over  sev- 
enteen years  to  traverse-the  distance  between  the  earth  and  the  sun  ;  how  long 
does  it  take  light  to  pass  over  this  distance  ?  (See  page  297.) 

State  the  most  obvious  distinctions  between  light  and  heat.  To  what  laws  are 
both  subject  ?  Could  there  really  be  any  light  without  eyes  ? 

Why  does  the  image  formed  by  a  lens  or  aperture  always  appear  inverted,  while 
that  reflected  from  a  mirror  does  not  ? 

When  a  ray  passes  from  a  rarer  to  a  denser  medium,  is  it  refracted  toward  or 
from  the  perpendicular  ? 

It  is  estimated  that  not  more  than  yfas  of  the  sun's  light  reaches  the  surface  of 
the  earth.  Why  is  this  ? 

The  planet  Venus  is  67,245,000  miles  from  the  sun  ;  Saturn  is  886,779,000.  How 
does  the  light  received  by  Venus  compare  with  that  received  by  Saturn  ? 

If  a  ray  of  light  from  the  sun  is  12,350  seconds  longer  in  reaching  Neptune  than 
Jupiter,  how  many  miles  farther  from  the  sun  is  Neptune  than  Jupiter  ? 

The  illuminating  powers  of  a  lamp  and  candle  are  as  10  to  1.  How  far  from  the 
lamp,  in  the  straight  line  joining  the  flames,  must  a  sheet  of  paper  be  placed 
to  be  equally  illuminated  by  both  ? 

If  you  can  just  see  to  read  by  moonlight  and  also  by  a  lamp  15  feet  away,  how 
much  brighter  is  the  moon  than  the  lamp  ? 

Compare  the  focal  lengths  of  two  lenses  whose  indices  of  refraction  are  respect- 
ively 1'5  and  2'4.  Of  what  materials  would  they  be  composed  ? 

The  index  of  refraction  from  water  into  turpentine  is  I'll.  What  is  the  index  of 
refraction  from  air  into  turpentine  ? 

What  would  be  the  result  if  the  solar  light  were  not  composed  of  various  colors  ? 
How  is  the  rainbow  produced  ?  Explain  fully  the  action  of  the  rain-drop  in 
producing  the  primary  and  secondary  bow. 

What  colors  would  apperr  black  in  a  room  to  which  the  sun's  light  is  admitted 
through  red  glass  ? 

Why  is  a  ball  fired  from  a  cannon  invisible  ?  Because  it  moves  with  such 
velocity  that  the  image  on  the  retina  does  not  remain  sufficiently  long  to  pro- 
duce an  impression.  It  has  been  photographed  by  the  instantaneous  process. 


SOUND. 

I   NATURE  OF  SOUND. 

Acoustics  is  that  branch  of  Natural  Philosophy  under 
which  is  studied  the  origin  and  nature  of  vibrations  causing 
sounds ;  the  transmission  of  these  vibrations  through  gases, 
liquids,  and  solids ;  and  the  mechanism  of  the  organs  of 
speech  and  hearing  viewed  as  acoustic  instruments. 

Sound  is  the  sensation  peculiar  to  the  ear.  It  is  caused 
by  the  vibration  of  the  nerves  of  hearing.  This  vibration 
generally  has  its  origin  in  some  vibrating  body,  such  as  a 
bell,  a  string,  or  an  organ-pipe,  surrounded  by  the  air.  Be- 
tween the  vibrating  body  and  the  drum-skin  of  the  ear,  the 
air  vibrates  in  unison  with  the  vibrating  body,  and  this  air, 

NOTE.— Let  the  pupil  provide  himself  with  the  articles  illustrated  in  the  intro- 
ductory group  above.  These,  in  connection  with  the  simple  apparatus  which  he 
can  put  together  in  accordance  with  instructions  given  in  the  text,  will  enable  him 
to  illustrate  the  principles  of  acoustics.  No.  1  is  a  violin-bow  ;  2,  an  A  tuning-fork 
mounted  on  resonant-box  ;  3,  a  C  tuning-fork  ;  4,  a  sound-lens  ;  5,  a  zither  ;  6,  a 
rotator  ;  and  7,  an  ordinary  bell.  The  outfit  will  be  furnished  by  Messrs.  James 
W.  Queen  &  Co.,  of  Philadelphia,  and  Mr.  Samuel  Hawkridge,  of  the  Stevens  In- 
stitute, at  price  stated  in  the  preface. 


MECHANISM   OP  HEARING. 


371 


touching  the  drum-skin  of  the  ear,  causes  the  latter  to  vi- 
brate in  unison. 

Mechanism  of  Hearing. — To  the  drum-skin  of  the 
ear,  or  membrane  of  the  tym'panuin,  is  attached  a  series  of 
three  little  bones  called  the  hammer  (H), 
the  anvil  (A),  and  the  stirrup  (S)  (see 
Fig.  256).  The  foot-plate  of  the  stirrup 
is  connected  with  an  oval  membrane 
which  closes  a  hole  in  the  inner  ear.  The 
inner  ear  is  filled  with  a  liquid,  in  which 
are  spread  out  the  filaments  of  the  audi- 
FIG.  256.-OSSICLES  m  tory  nerve,  or  nerve  of  hearing.  The 
drum-skin,  vibrating  in  unison  with  the 
vibrating  body  and  the  air  surrounding  it,  sends  vibra- 
tions through  the  little  ear-bones  (ossicles)  to  the  liquid 
and  nerve-fibers  in  the  inner  ear,  and  the  trembling  of 
these  nerve-fibers  causes  the  sensation  called  Sound. 

Fig.  257  illustrates  the  parts  of  the  human  ear. 
Waves  of  sound  are  collected  by  the  trumpet- 
shaped  external  ear  or  pinna  (1)  and  directed  through 
the  auditory  canal  (2,  3)  to  the  drum  (4).  The  ham- 


2  7^ 

FlG.  257.— GrENERAL  VlEW  OF  THE  ORGAN  OF  HEARING. 

1,  pinna ;  2,  3,  auditory  canal,  with  openings  of  wax  glands  ;  4,  membrana 
tympani,  or  drum-skin  ;  5,  portion  of  anvil ;  6,  hammer  ;  7,  handle  of  hammer 
applied  to  internal  surface  of  drum-skin,  which  it  draws  inward  ;  8,  Eustachian 
tube  ;  9,  10,  11,  semicircular  canals  ;  12,  cochlea  ;  13,  14,  auditory  nerve. 


372  SOUND. 

mer-bone  (6)  is  shown  connected  with  the  drum-skin ;  the  stirrup- 
bone  is  attached  to  an  oval  membrane  closing  a  hole  in  the  vestibule 
of  the  inner  ear.  From  this  vestibule,  the  cavity  opens  into  the  semi- 
circular canals  (9,  10,  11),  and  also  into  a  spiral  cavity  (12),  which  so 
resembles  a  snail's  shell  as  to  be  called  by  its  Latin  name,  cochlea.  In 
the  cochlea  are  the  filaments  of  the  auditory  nerve  (13,  14). 

Sound  implies  Vibration. — To  show  that  we  have  de- 
fined sound  correctly,  and  truthfully  represented  its  nature, 
we  must  prove — 

1.  That  whenever  we  perceive  a  sound,  some  body,  either 
a  solid,  a  liquid,  or  a  gas,  is  in  vibration. 

2.  That  the  air  surrounding  the  vibrating  body  is  also 
vibrating  in  unison  with  it. 

3.  That  the  drum-skin  and  bones  of  the  ear  are  at  the 
same  time  vibrating  with  the  vibrating  body  and  the  air. 

The  Vibrating  Body. — Fig.  258  repre- 
sents a  tuning-fork  mounted  on  a  resonant- 
box.  If  we  draw  a  violin-bow  across  one  of 
the  prongs  of  the  fork,  or  strike  it  with  a 
stick  covered  with  leather,  we  hear  a  sound. 
The  fork  is  now  in  vibration,  for  if  we  touch 
the  face  of  one  prong  with  a  little  ball  of 
cork  suspended  to  a  fine  silk  fiber,  we  shall 
see  the  cork  violently  repelled  from  the  prong, 
and  these  blows  against  the  cork  ball  will  be 
visible  until  the  sound  becomes  almost  too  feeble  to  be 
heard.  The  cork-pendulum  will  in  like  manner  show  the 

vibration  of  a  bell,  a  fin- 
ger -  bowl,  a  plate  or  rod, 
a  stretched  membrane,  a 
string,  etc. 

Further,  unscrew  the  fork 
from  its  resonant-box  and  ce- 
ment to  one  of  its  prongs  a  tri- 
angular  piece  of  thin  copper-foil. 

Fio.  259.— PROOF  OF  VIBRATION  OP        Strike  the  fork  with  a  stick,  and 
TUNING-FORK.  draw  along,  under  the  tip  of  the 


ESSENTIAL  CONDITIONS  OF  SOUND. 

foil,  a  piece  of  glass  blackened  with  camphor-smoke.  The  trace  of 
the  point  of  the  foil  will  appear  as  in  Fig.  259,  showing  that,  while  the 
glass  was  drawn  along,  the  prong  went  many  times  to  and  fro  in  a 
direction  at  right  angles  to  its  path.  If  we  had  armed  each  prong 
with  its  own  piece  of  foil,  we  should  have  had  a  double  trace,  like  that 
shown  in  Fig  260.  Such  a  trace  proves  that  the  prongs,  in  vibrating, 
approach  each  other  and  then  recede,  and  that  one  prong  makes  the 
same  trace  as  the  other. 

The  Vibrating  Medium. — If  a  membrane  of  paper  or 
gold-beater's  skin  be  stretched  on  a  frame,  and  a  few  fine 
particles  of  sand 
be  placed  on  it, 
the  sand  will 

FIG.  260. — VIBRATIONS  OP  BOTH  PRONGS  REGISTERED. 

jump  up  and  down 

when  the  membrane  is  held  in  the  air  at  a  distance  from 
a  vibrating  and  sounding  body.  If  we  stretch  a  piece  of 
linen  paper  over  the  mouth  of  a  tumbler,  and  then  cut  away 
part  of  the  paper  till  the  tumbler  gives  forth  a  loud  sound 
when  the  fork  is  brought  over  the  opening,  as  shown  in 
Fig.  261,  we  may  place  the  tumbler  in  any  part  of  the  room, 
and  sand  on  the  paper  will  dance  whenever  the  fork  is 
sounded  on  its  resonant-box,  or  when  an 
organ-pipe  is  blown  which  gives  the  same 
note  as  the  fork. 


If  two  bodies  vibrate  the  same  number  of  times 
a  second,  and  one  of  them  is  sounded,  the  aerial 
vibrations  caused  by  this  one  will  set  in  vibration 
the  other  body,  even  at  a  considerable  distance. 
This  phenomenon  is  a  general  one,  and  is  called  co- 
vibration.  It  may  be  readily  exhibited  by  placing  two  tuning-forks, 
which  give  the  same  note,  on  their  resonant-boxes  and  at  a  distance  of 
several  feet  from  each  other.  If  one  of  the  forks  be  sounded,  the  other 
will  enter  into  vibration. 

The  Vibrating  Ossicles  of  the  Ear. — In  Fig.  262  are 
presented  traces  obtained  by  Konig,  of  Paris,  on  attaching 
a  delicate  bristle  to  the  several  bones  of  the  ear.  This  bris- 
tle was  in  contact  with  the  surface  of  a  revolving  cylinder 


374  SOUND. 

covered  with  lamp-black.  When  an  organ-pipe  or  fork  was 
sounded  in  the  air,  the  bristle  vibrated  with  the  bone  to 

which  it  was  fastened,  and 
these  vibrations  were  traced 
by  the  bristle  on  the  cylin- 
der. 

The     traces     obtained 
were    found    to    have    the 

FIG.  262. — REGISTERED  VIBRATIONS  OF 

OSSICLES.  same  number  of  flexures  in 

1,  Vibrations  drawn  with  a  bristle  at-  them,  in  a  given   length,  as 

tached  to  the  hammer  of  the  human  ear ;  j.v  -j          •        •>, 

2,  4,  vibrations  of  two  organ-pipes  traced  the     traC6     made     «™tt* 

with  a  bristle  attached  to  the  anvil ;  3,  neOUSly  On  the  Cylinder  by 
vibrations  of  a  bristle  attached  to  the  stir-  second  f  k  in  t  jth 

rup  of  the  ear  of  a  goose. 

the    first.       Thus    it    was 

clearly  shown  that  the  parts  of  the  ear  vibrate  in  unison 
with  the  sounding  body,  as  well  as  with  the  air  striking  the 
drum-skin. 

Our  knowledge  of  sounds  is  wholly  due  to  the  interpretation  of 
vibrations  by  the  nerves  of  the  ear.  Hence  a  deaf-mute  can  have  no 
conception  of  sounds.  Vibrations,  it  is  true,  are  felt,  not  only  by  the 
hand,  but,  in  case  of  deep  tones,  by  the  whole  frame.  Persons  born 
deaf  may  thus  experience  pleasure  on  the  performance  of  music.  Feel- 
ing vibrations,  however,  is  very  different  from  hearing  sound. 

Air  is  not  the  only  Medium  of  Transmission  of 

sound.  If  the  foot  of  the  tuning-fork  be  screwed  into  a 
disk  of  wood,  and  this  disk  placed  in  contact  with  a  column 
of  water  contained  in  a  jar  which  rests  on  the  resonant-box 
of  the  fork,  we  shall  hear,  when  the  fork  is  struck,  a  sound 
caused  by  the  transmission  of  the  vibrations  of  the  fork 
through  the  water  to  the  resonant-box. 

If,  while  bathing,  you  hold  your  head  under  the  water 
for  a  moment,  you  will  be  able  to  hear  distinctly  a  sound 
produced  beneath  the  surface  at  a  considerable  distance. 
This  proves  that  water  is  a  transmitting  medium. 

Fish  are  provided  with  organs  of  hearing,  which  are  affected  only 
by  the  vibrations  of  the  element  in  which  they  live.  Such  vibrations 


TRANSMISSION  BY  LIQUIDS  AND  SOLIDS.         375 


may  be  communicated  to  the  water  of  a  stream  by  persons  walking 
along  the  bank,  and  are  immediately  appreciated  by  the  nerves  of  fishes 
insensible  to  sounds  made  in  the  air. 

Further,  if  a  long  wooden  rod  be  placed  against  the  head,  and  the 
other  end  of  the  rod  be  brought  in  communication  with  the  foot  of  the 
vibrating  fork,  we  shall  hear  a  sound  caused  by  the  passage  of  the 
vibrations  of  the  fork  through  the  wood,  and  through  the  skin  and 
bones  of  the  head,  to  the  nerves  of  the  ear.  The  conducting  power  of 
seasoned  wood  fur- 
nishes a  ready  test  by 
which  a  flaw  may  be 
detected  in  a  beam ; 
rotten  wood  interferes 
noticeably  with  the 
transmission  of  sound. 

Attach  to  the  foot 
of  the  tuning-fork  a 
string  held  between" 
the  teeth.  When  the 
string  is  stretched  be- 
tween the  teeth  and 
the  fork,  and  the  lat- 
ter is  vibrated,  the 
sound  of  the  fork  will 
be  heard.  The  String 
Telephone,  or  Lovers' 
Telegraph,  illustrates, 
in  an  interesting  man- 
ner, the  transmission 
of  sound  by  a  cord. 
It  may  be  cheaply 
made  by  removing  the 
bottoms  from  two 
small  tin  cups  and 
supplying  their  places 

with  pieces  of  rubber  or  parchment,  tightly  wound  on  and  connected 
with  the  ends  of  a  long  cord.  If  the  cord  be  drawn  tight,  a  conver- 
sation may  be  carried  on  between  persons  a  number  of  rods  apart,  by 
using  one  cup  as  a  mouth-piece  and  listening  at  the  other,  as  shown 
in  Fig.  263.  Small  pasteboard  boxes  may  be  used  instead  of  the  cups. 

An  approaching  locomotive  can  be  heard  at  a  great  distance  by 
placing  one's  ear  on  the  rails.    The  American  Indians  knew  by  expe- 


FIG.  263.— THE  STRING  TELEPHONE. 


376  SOUND. 

rience  the  facility  with  which  solids  transmit  sounds,  and  were  in  the 
habit  of  applying  their  ears  to  the  earth  when  they  suspected  the  ap- 
proach of  an  enemy,  or  wanted  a  more  distinct  impression  of  any  sound 
that  attracted  their  attention. 

Sound  not  produced  in  a  Vacuum. — As  sound  thus 
implies  the  vibration  of  air  or  some  other  material  substance, 
there  can  be  no  sound  in  a  vacuum.  A  bell  rung  in  the 
exhausted  receiver  of  an  air-pump  can  not  be  heard.  The 
absence  of  atmosphere  on  the  moon's  surface  imports  per- 
petual silence. 

To  illustrate  this  principle  simply,  pour  a  little  water  into  your 
glass  flask,  close  the  flask  with  an  India-rubber  cork  having  two  holes, 
through  one  pass  a  glass  rod,  and  by  means  of  a  piece  of  rubber 
tubing  attach  to  the  end  of  the  rod  a  toy  bell.  Now  apply  heat  until 
the  water  boils.  The  steam  will  expel  the  air,  and,  if  you  close  the 
second  hole  in  the  rubber  cork  with  a  glass  stopper,  you  will  have  a 
fair  vacuum  in  the  flask  when  the  steam  condenses.  If  the  flask  be  now 
shaken,  the  sound  of  the  bell  will  be  extremely  feeble,  if  not  inaudible. 

Velocity  of  Sound. — The  vibrations  causing  sound  are 
transmitted  by  air  at  a  temperature  of  32°  Fahr.,  with  a 
velocity  of  1,090  feet  a  second.  With  every  rise  of  1°,  the 
velocity  of  sound  increases  by  one  foot.  Thus,  at  a  tem- 
perature of  85°  (53°  above  32°)  the  velocity  of  sound  in  air 
is  1,143  feet  a  second.  At  60°  Fahr.,  sound  travels  a  mile  in 
about  4f  seconds. 

The  velocity  of  sound  in  air  is  thus  less  than  that  of 
light;  it  is  also  less  than  that  of  a  bullet.  A  rifle-ball 
reaches  a  deer  before  he  hears  the  report ;  but  the  flash  is 
seen  before  the  bullet  strikes.  Water-fowl  learn  to  dive, 
and  wary  game  to  dodge,  at  sight  of  the  flash,  and  so  escape. 
With  the  old  flint-lock  fowling-piece,  the  flash  in  the  pan 
gave  longer  notice  of  danger. 

The  velocity  of  sound  in  oxygen  gas,  at  32°,  is  1,040  feet  a  second. 
In  hydrogen,  it  is  4,160  feet,  or  four  times  as  great.  As  a  cubic  foot  of 
hydrogen  weighs  only  ^  as  much  as  a  cubic  foot  of  oxygen,  it  follows 
that  the  speed  of  sonorous  vibrations  through  gases  varies  inversely  as 


VELOCITY   OF  SOUND. 

the  square  roots  of  the  weights  of  equal  volumes  of  the  gases,  or,  in 
other  words,  in  the  inverse  ratio  of  the  square  roots  of  their  densities. 

Sound  travels  more  rapidly  in  liquids  and  in  solids  than 
in  air.  The  velocity  of  sound  in  water  is  about  4£  times  as 
great  as  in  air.  In  steel,  it  is  about  10J  times  as  great. 

The  Velocity  of  Sound  is  the  same  for  all  Notes, 
whether  high  or  low.  This  was  shown  by  Biot  (be-or),  who 
found  that  melodies  played  at  one  end  of  the  long  aqueduct 
of  Paris  reached  the  other  end  without  alteration.  This 
could  not  have  been  if  the  sounds  composing  the  melodies 
had  different  rates  of  velocity. 

QUESTIONS.— What  is  Acoustics  ?  Define  Sound.  By  what  is  sound  caused  ?  Ex- 
plain fully  the  mechanism  of  hearing,  drawing  on  the  blackboard  a  diagram  of 
the  auditory  canal  and  inner  ear.  What  three  vibrations  are  implied  in  the 
sensation  of  sound  ?  Prove  that  the  sounding  body  vibrates  by  an  experiment 
with  the  tuning-fork  ;  with  a  common  bell.  Why  is  the  bell  stopped  from  ring- 
ing by  touching  it  with  the  finger.  Moisten  the  edge  of  a  glass  finger-bowl  or 
thin  goblet,  and  move  the  finger  rapidly  around  it ;  why  will  it  give  forth  a 
musical  sound  ?  Strike  your  tuning-fork,  and  hold  a  card  near  it ;  why  will 
you  hear  a  continuous  tapping  ?  Do  you  know  how  the  vibrations  of  both 
prongs  may  be  registered  ?  Prove  that  the  air  is  in  vibration  when  we  hear  a 
sound.  Explain  the  phenomenon  of  co-vibration.  What  interesting  experi- 
ments show  that  the  ossicles,  or  little  bones  of  the  ear,  vibrate  in  unison  with 
the  air  ?  Explain  the  difference  between  feeling  vibrations  and  hearing  sounds. 

Can  you  think  of  any  causes  of  deafness  ?  Whatever  interferes  with  the  trans- 
mission of  vibrations  to  the  nerves  of  the  ear  causes  deafness,  as  ceru'men  or 
wax  in  the  auditory  canal,  perforation  of  the  drum-skin,  or  destruction  of 
the  little  bones  by  inflammation  in  scarlet  fever.  In  order  that  hearing  may 
be  perfect,  the  cavity  of  the  middle  ear,  which  is  spanned  by  the  three  bones, 
must  contain  warm  air.  Nature  provides  for  its  free  admission  through  the 
Eustachian  (yu-sta'ki-an)  tube  (see  Fig.  257,  No.  8),  which  connects  the  middle 
ear  with  the  throat.  Why,  then,  is  temporary  deafness  produced  by  a  cold  ? 
Can  you  think  of  a  reason  why  exposure  to  loud  noises  may  be  injurious  to 
hearing  ?  Why,  boxing  the  ears  ?  Surf -bathing  ?  A  severe  blow  on  the  head  ? 

Is  air  the  only  medium  of  transmission  of  sound  ?  What  evidence  is  there  that 
water  transmits  vibrations  ?  Do  fish  hear  ?  How  ?  Describe  an  easy  method 
of  detecting  a  rotten  spot  in  a  wooden  beam.  What  is  the  string  telephone  ? 
Why  can  you  hear  a  train  coming  by  placing  your  ear  on  the  rail,  when  the  air 
conveys  no  perceptible  sound  of  its  approach  ?  How  can  you  show  that  sound 
is  not  transmitted  in  a  vacuum  ?  State  the  velocity  of  sound  at  50*  Fahr. ;  at 
70*.  What  familiar  example  can  you  give  to  prove  that  sounds  of  all  kinds 
travel  at  the  same  rate  ?  Do  all  substances  transmit  sound  with  the  same 
velocity  ?  What  is  the  velocity  of  sound  in  water  ?  In  steel  ?  Standing  in  a 
lumber-camp,  at  some  distance  from  a  wood-chopper,  I  hear  the  blow  of  his 
axe  2i  seconds  after  I  see  the  chips  fly.  Suppose  the  temperature  to  be 
34°  Fahr.,  how  many  rods  am  I  from  the  chopper  ? 
25 


378  SOUND. 


PROPAGATION   OF  SOUND.— WAVE-MOTION. 

Principle  of  Transmission. — Before  beginning  the 
study  of  the  nature  of  sound  transmission,  it  will  be  neces- 
sary to  understand  the  following  experiment  with  glass 
balls,  showing  how  vibrations  travel  through  elastic  bodies. 
Fig.  264  represents  a  wooden  railway  about  6  feet  long.  It 


FIG.  264. — ILLUSTRATING  HOW  VIBRATIONS  TRAVEL  THROUGH  ELASTIC  BODIES. 

is  made  of  thin  strips  of  pine,  placed  side  by  side,  about  an 
inch  apart,  and  joined  by  cross-pieces.  The  cross-piece  at 
the  center  is  screwed  down  to  the  table,  and  the  ends  of  the 
elastic  slips  are  then  raised  on  blocks.  Place  a  few  large 
glass  marbles  in  the  middle  of  this  curved  railway,  and  then 
bring  one  to  the  end  and  let  it  roll  down  against  the  others. 
The  marbles  will  remain  stationary  except  the  farthest 
one,  which  will  fly  up  the  incline  toward  the  other  end  of 
the  railway  and  then  roll  back  again,  causing  the  first 
marble  to  ascend  the  incline  on  the  right.  This  action  will 
continue  till  friction  brings  the  marbles  to  rest. 

The  marbles  employed  in  the  experiment  are  very  elastic.  This  is 
proved  by  rubbing  a  slab  of  stone  with  a  mixture  of  oil  and  red  lead 
and  placing  a  marble  on  it.  The  marble  will  be  marked  by  a  small 
circle  of  red ;  but  if  we  allow  it  to  fall  on  the  stone,  a  much  larger 
circle  of  red  will  be  made,  showing  that  the  marble  must  have  flattened 
when  it  struck,  as  it  evidently  touched  a  larger  surface  of  the  stone. 

The  first  marble  rolls  down  the  railway  and  strikes  the  second, 
which  is  thus  flattened  between  1  and  3,  as  shown  in  Fig.  265.  Marble 
No.  2  at  once  springs  back  into  its  former  spherical  figure,  and  in  so 
doing  brings  No.  1  to  rest  and  flattens  No.  3,  as  shown  in  Fig.  266. 
Marble  No.  3  then  springs  to  its  former  spherical  figure,  bringing  to 


TRANSMISSION  OF  SONOROUS  VIBRATIONS.       379 

rest  No.  2  and  flattening  No.  4.  Thus  each  marble  receives  the  blow 
of  the  marble  behind  and  passes  it  on  to  the  one  in  front,  and  we  have 
a  series  of  contractions  and  expansions  running  rapidly  through  the 

_  mnoooo^  _  omonoo_ 

FIG.  265.  FIG.  266. 

row.  When  the  last  marble  is  flattened,  it  at  once  expands,  bringing 
the  one  behind  it  to  rest,  and,  having  nothing  in  front,  it  is  shot  up 
the  railway. 

Compression  and  Expansion  in  a  Tube. — Similar 
actions  take  place  in  successive  portions  of  air  as  sonorous 
vibrations  traverse  them.  In  Fig.  267,  a  long  tube,  dfge,  is 
open  at/#  and  closed  at  the  other  end  by  a  piston  «,  which 
can  be  moved  forward  and  backward  in  the  tube.  Suppose 
the  piston  a  to  move  quickly  forward  to  the  position  b ;  then, 
if  the  air  were  inelastic  and  incompressible,  a  portion  of  the 
column  of  air  equal  to  that  from  a  to  b  would  be  pushed  ou*  of 
the  end  of  the  tube  at  fa. 

n.     7) c C' 


As  the  air  is  elastic,  it  is       d~ 

compressed  by  the  forward     ~^~_ 

motion  of  the  piston ;   but       FlG.  ^.-TRANSMISSION  JN  A  TUBE.  J 

only  to   a   certain   distance 

beyond  b  is  it  so  compressed  at  the  instant  the  piston  has 

reached  b. 

The  length  be  of  this  compression  is  found  thus :  The  compression 
can  travel  only  as  fast  as  the  velocity  of  sound,  which  at  40°  Fahr.  is 
1,100  feet  a  second  ;  so  that  if  the  piston  takes  y^  of  a  second  to  go 
from  a  to  b,  the  length  of  the  compressed  air,  b  to  c,  is  -^  of  1,100,  or 
11  feet.  If  the  piston  takes  -nf^  of  a  second  to  go  from  a  to  b,  then 
the  depth  of  the  compressed  air  is  y^  of  1,100  feet,  or  1^-  feet. 

At  the  moment  the  piston  a  reaches  5,  we  have  compressed  air  in 
the  tube  from  b  to  c.  This  compressed  air  is  elastic — like  a  bent 
spring,  or  one  of  the  glass  marbles  used  in  the  previous  experiment ; 
it  at  once  expands,  and  in  the  same  time  (assumed  to  be  y^  of  a 
second)  that  was  occupied  in  its  compression.  It  presses  against  the 
interior  of  the  tube  and  against  the  piston  at  b ;  but  these  do  not  yield. 
It  also  presses  and  at  the  same  time  expands  in  a  forward  direc- 


380  SOUND. 

tion,  toward  the  mouth  of  the  tube,  and  in  the  next  ToW  of  a  second 
it  has  by  this  expansion  compressed  another  mass  of  air,  c  to  c',  equal 
in  length  to  b  c.  In  compressing  the  column  c  c',  the  air  in  the  col- 
umn b  c  expanded  to  its  natural  volume.  The  column  c  c'  next  ex- 
pands as  did  the  column  b  c.  But  it  can  not  expand  backward,  be- 
cause the  column  of  air  b  c  has  expanded  with  rapidity  to  its  natural 
volume  in  compressing  c  c',  and  therefore  tends  by  its  momentum  (like 
a  swinging  pendulum)  to  expand  still  further — which  action  just  bal- 
ances the  backward  expansion  of  the  air  in  c  c',  so  that  the  column  of 
air  b  c  now  acts  like  the  solid  piston  against  the  column  c  c'.  Thus  the 
compression  is  sent  through  the  air  of  the  tube  with  a  velocity  equal 
to  that  of  sound,  and  by  a  series  of  actions  similar  to  those  which  took 
place  in  the  row  of  glass  balls  in  the  previous  experiment. 

If  we  now  suppose  the  piston  to  move  in  y^  of  a  second  from  b 
back  to  a,  the  air  from  a  to  c  will  be  rarefied,  and  the  actions  follow- 
ing will  be  similar  to  those  which  took  place  with  the  column  of  con- 
densed air,  only  a  pulse  of  rarefied  air  will  now  travel  through  the 
tube  instead  of  one  of  condensed  air. 

The  Effect  of  Compressing  Air  is  to  bring  its  mol- 
ecules nearer  together,  while  rarefaction  separates  them. 
Hence,  if  we  imagine  the  piston  to  vibrate  regularly  from  a 
to  b  and  back  from  b  to  «,  like  a  pendulum,  or  as  the  prong 
of  a  tuning-fork  really  does,  we  shall  have  the  molecules  of 
the  air  in  the  tube  making  short  vibrations  forward  and 
backward,  each  molecule  having  the  motion  of  a  pendulum. 

If  the  ear  be  placed  at  the  mouth  of  the  tube,  we  shall  hear  a 
musical  note  corresponding  in  sound  to  that  of  a  fork  making  1,000 
vibrations  a  second. 

Sound-Waves  in  the  Air. — If  instead  of  a  piston  mov- 
ing to  and  fro  in  a  tube  we  have  a  tuning-fork  or  other 
musical  instrument  vibrating  in  the  open  air,  the  condensa- 
tion and  rarefaction  of  the  air  will  not  be  confined  to  one 
direction,  as  in  the  tube,  but  will  spread  all  around ;  so  that 
we  shall  have  spherical  shells  of  compressed  and  rarefied  air 
continually  following  one  another,  as  they  expand  outward 
in  regular  order  and  motion,  like  the  outward  movement  of 
circular  water-waves  around  the  place  where  a  pebble  has 
been  dropped  into  a  pond. 


NATURE  OF  A   SOUND-WAVE.  381 

The  depth  of  air  embracing  any  condensed,  and  the  ad- 
joining rarefied,  shell  of  air,  is  called  a  sound-wave.  This 
sound-wave  is  entirely  different  from  a  water-wave,  in  which 
the  water  vibrates  up  and  down  in  a  direction  perpendicular 
to  that  of  the  wave's  progress.  In  a  sound-wave  the  vibra- 
tory motions  of  the  air  are  not  perpendicular  to,  but  in  the 
same  direction  as,  the  direction  of  motion  of  the  sound- 
wave. 

To  represent  a  Sound-Wave,  a  curve  is  used  called  the 
sinusoidal  curve  (see  Fig.  268).  In  this  figure,  the  line  A  B, 
which  is  the  axis  of  the  curve,  represents  the  direction  of 
the  sound  vibrations.  The  lengths  of  lines  drawn  perpen- 
dicularly from  this  axis  to  any  point  of  the  curve  represent 
the  amount  of  compression  or  of  rarefaction  of  the  air. 
Thus,  at  the  points  A,  C,  and  i 

B,  the  air   is   neither  com-        Jk^  ~^\ 

pressed  nor  rarefied.      At  h    A/_ I — 1 Np    e, — 5 -78 

the  length   of  the  line  g  Ji  ^^^/ 

represents    the    amount    of  *     a 

Compression,    while    at  f  the  FlG-  ^-REPRESENTATION  OF  A 

'  /  SOUND-WAVE. 

length    e  f  represents    the 

amount  of  rarefaction — lengths  above  the  line  being  as- 
sumed to  stand  for  compressions,  and  lengths  below  the 
line  for  rarefactions.  The  whole  length  A  to  B  is  a  wave- 
length, while  the  length  A  to  C,  j  to  &,  or  0  to  B,  is  a  half- 
wave  length. 

Although  the  nature  of  a  sound-wave  has  been  known  since  the 
time  of  Newton,  and  although  this  curve  representing  its  nature  has 
been  used  during  almost  as  long  a  period,  yet  many  have  confounded 
the  curve — a  mere  symbol — with  the  sound-wave  itself,  and  have  been 
led  into  gross  errors  by  supposing  a  sound-wave  to  be  composed  of 
waves  shaped  like  this  curve  and  progressing  through  the  air  with 
heaps  and  hollows  like  the  waves  of  the  ocean. 

The  Nature  of  a  Sound-Wave,  and  the  manner  in 
which  it  travels  through  an  elastic  medium,  are  nicely  rep- 
resented in  an  ingenious  apparatus  invented  by  Crova.  In 


382 


SOUND. 


the  illustration  on  page  370,  is  represented  (No.  6)  a 
cardboard  disk  mounted  on  the  axle  of  a  rotating 
machine.  Upon  this 
disk  are  drawn  24  cir- 
cles of  different  di- 
ameters, having  their 
centers  on  the  smaller 
circle  C,  shown  in 
Fig.  269. 

These  circles  arc 
drawn  as  follows ; 
Around  the  center  of 
the  disk,  describe  the 
small  circle  C  (Fig.  270) 

and  divide  its  circumfer- 

FIG.  269.— CROVA'S  DISK,  £  SIZE. 
ence  into  12  equal  parts. 

Draw  the  line  A,  B,  24.  Take  the  length  A  B  with  dividers,  hav- 
ing a  drawing-pen  with  India-ink  in  it,  and,  placing  the  point 
of  the  dividers  on  division  1  of  the  small  circle,  describe  on  the 
cardboard  disk  a  circle  having  a  radius  of  A  B.  Then  take  a 
radius  A  to  1,  and  with  center  2  on  small  circle  describe  another 
circle.  Then  with  radius  A  2  and  center  3  on  small  circle,  de- 
scribe on  the  cardboard  a  third  circle,  and  so  on,  taking  radii 
successively  greater  by  one  division  on  the  scale  A  24,  and  draw- 
ing circles  with  centers  on  successive  points  of  the  circle  C. 

A  piece  of  cardboard  having  a  slit  cut  out  of  it  (shown  in 
No.  6,  page  370)  is  placed  horizontally  so  that  only  short  lines 
of  the  circles  are  seen  in  the  slit.  On  rotating  the 
disk,  these  short  lines,  which  stand  for  molecules 
of  the  air,  will  be  seen  to  move  backward  and  for- 
ward like  so  many  little  pendulums,  producing  in 
the  row  of  lines  a  horizontal,  worm-like  movement. 
This  movement  causes  a  wave  to  appear  at  one  end 
of  the  slit,  move  along,  and  disappear  at  the  other 
end,  by  the  successive  crowding  together  (condensation)  and 
separation  (rarefaction)  of  the  row  of  dots. 

If  we  examine  closely  the  cause  of  this  progressive 
wave-motion,  we  shall  see  that  each  dot  moves  only 
backward  and  forward  ;  but  as  these  motions  of  vibra- 


FIG.  270. 


WAVE-MOTION. 


383 


tion  are  successive  and  not  in  unison,  it  is  evident  that  we 
have  a  series  of  condensations  of  the  dots,  alternated  with  a 
series  of  separations  or  rarefactions,  following  one  another  in 
a  uniform  movement  and  order,  and  progressing  along  the 
slit.  This  pictures  to  the  mind  the  motion  of  successive 
condensations  and  rarefactions  in  the  air  as  sonorous  vibra- 
tions pass  through  it. 

In  an  Experiment  described  by  C.  J.  Woodward,  of 
Birmingham,  England,  the  same  progressive  motion  of  the 
condensations  and  rarefactions  of  a  sound-wave  is  obtained 
directly  from  the  vibrations  of  small  pendulums. 

A  row  of  pendulums  of  equal  length  is  suspended  from  a  rod,  A 
B  (Fig.  272).  In  order  to  start  the  pendulums,  the  bobs  are  placed 
against  an  angular-shaped  board  F  C  I),  the 
rod  being  held  in  a  plane  slightly  behind  the 
plane  of  the  board.  If,  now,  the  rod.  and  pend- 
ulums are  raised  together  vertically,  I  will  first 
swing,  then  Jc,  and  so  on,  till  all  are  free.  When 

FIG.  272  —WAVE  -  MOTION   the  pendulums  are  raised  with  a  uniform  ve- 
ILLUSTRATED.  locity,  then  each  pendulum  starts  at  an  equal 

period  of  time  after  the  one  that  is  next  to  it. 

The  result  is  that  a  wave-motion  is  seen  to  run  along  the  line  of  bobs 
as  they  vibrate  to  and  fro. 

Such  an  arrangement  has  been  used  to  illustrate  wave-motion,  as 
each  bob  moves  with  harmonic  motion — i.  e.,  a  motion  like  a  pendu- 
lum's ;  but  it  does  not  illustrate  directly  those  compressions  and  rare- 
factions whereby  sound  is  propagated. 
A  change  of  position  of  the  rod,  how- 
ever, at  once  makes  it  do  so.  If,  while 
the  pendulums  are  vibrating,  the  rod 
from  which  they  are  suspended  be  turned 
in  the  horizontal  plane  through  a  right 
angle,  the  direction  of  the  swing  of  each 
pendulum  is  not  changed,  and  all  the 
pendulums  swing  in  the  same  plane. 
This  will  become  clear  from  Fig.  273, 
where  the  pendulum-bobs  viewed  along 
O  X  appear  to  trace  out  wave-motion.  The  relative  position  of  the 
bobs,  after  the  rod  which  supports  them  is  turned  through  a  right 
angle,  is  shown  along  0  Y.  The  motion  then  illustrates  mechani- 


FIG.  273. — PROPAGATION  OP 
A  SOUND-WAVE. 


384  SOUND. 

cally  those  movements  of  air  particles  which,  when  in  compression 
and  rarefaction,  propagate  a  sound-wave. 

Pendulums  made  of  bullets  1*5  centimetres  in  diameter,  suspended 
from  threads  30  centimetres  long,  were  found  to  answer  the  purpose. 

Interference   of  Sound.  —  If   a  condensed  half-wave 
meets  a  rarefied  half-wave,  and  these  half-waves  have  the 
same  length  and  the  same  extent  of  vibratory  motion,  then 
they  must  neutralize  each  other's  action  in  that  part  of  the 
air  where  they  meet,  and  no  motion  results  from  their  com- 
bined action.     The  reason  of  this  is  that,  while  the  con- 
densed half  -wave  tends  to  force  the  molecules  of  air  closer 
together,  the  rarefied  half-  wave  tends  with  an  equal  energy 
to  separate  them  ;  so  they  remain  at  rest,  and  at  the  place  of 
meeting  of  the  half-waves  there  is  no  sound.     This  fact  is 
made  apparent  in  many  experiments. 

The  trace  obtained  simultaneously  from  the  two  prongs 
of  a  vibrating  fork  (see  Fig.  260)  shows  that  these  prongs 
move  apart  and  then  draw  together,  each  making  the  same 
_,-  ------  ^  number   of   vibrations   in   the  same 

time.  When  the  prongs  of  a  fork 
approach  each  other,  the  air  is  con- 
densed in  front  of  the  space  between 
the  prongs,  and  rarefied  in  front  of 
the  flat  faces  of  the  prongs  ;  and 
when  the  prongs  separate,  the  air  is 
rarefied  in  front  of  the  space  between 
FIG.  274.  -INTERFERENCE  OF  the  prongs,  and  condensed  in  front 


SOUND    ILLUSTRATED     BY    A     Qf   the  flat  faceg   Qf  the  pr0ngs. 

VIBRATING  TUNING-FORK.  . 

we  nave  at   the   same  instant  lour 

equal  actions,  whose  combined  effect  on  the  air  is  shown  in 
Fig.  274  when  we  look  down  upon  the  tops  of  the  prongs  c  c. 
Imagine  the  prongs  swinging  away  from  each  other  in  their  vibra- 
tion. Then  the  action  of  the  faces  c  c  on  the  air  is  to  condense  it,  and 
this  condensation  tends  to  spread  all  around  the  fork;  but  by  the 
same  movement  of  the  fork  the  space  r  r  between  the  prongs  is  en- 
larged, and  hence  a  rarefaction  is  made  there,  and  this  rarefaction  also 
tends  to  spread  all  around  the  fork. 


INTERFERENCE  OF   SOUND. 


385 


Now,  as  the  condensation  produced  at  c  c  and  the  rarefaction  at 
r  r  spread  with  the  same  velocity,  it  follows  that  they  must  meet  along 
the  dotted  lines  qqqq,  drawn 
from  the  edges  of  the  fork 
outward,  and  on  the  planes  in- 
dicated by  these  dotted  lines, 
there  will  be  no  motion  of  the 
air.  This  fact  is  shown  by 
slowly  rotating  the  fork  around 
its  length  as  a  vertical  axis, 
while  the  fork  is  held  near  the 
ear.  Whenever  the  planes  qqqq 
are  opposite  the  ear,  there  is 
silence.  In  other  positions  of 
the  fork,  sound  is  heard.  In 
one  rotation  of  the  fork,  there 
will  be  four  places  of  silence. 

The  same  fact  is  also  ap- 
parent on  rotating  the  fork 
over  a  large  tumbler  whose 
mouth  is  partly  closed  by  a 
piece  of  glass.  The  size  of  the 
opening  in  the  tumbler  is  pre- 
viously so  adjusted  that  the 
air  in  the  tumbler  strongly  re- 
sounds to  the  vibrations  of  the 
fork.  This  experiment  is 
shown  in  Fig.  275. 

If  we  adjust  the  openings 
in  two  wide-mouthed  bottles 
to  resound  to  the  fork,  and 
then  arrange  the  bottles  and 
fork  as  shown  in  Fig.  276,  we 
shall  have  silence  when  the 
fork  is  so  placed  that  each  time 
a  condensation  enters  one  bot- 


FIG.  275.— ILLUSTRATING  INTERFERENCE. 


tie  a    rarefaction    enters 
other,  or  vice  versa. 


the 


Beats  of  Sound  pro- 
duced by  Interference. 

— Interference  of  sound  is 


FIG.  276. — INTERFERENCE  OF  SONOROUS 
VIBRATIONS. 


386  SOUND. 

also  produced  when  two  sounds  fall  at  the  same  time  on  the 
ear,  and  one  of  these  sounds  is  slightly  natter  or  sharper ' 
than  the  other.  This  phenomenon  is  always  observed  when 
two  organ-pipes,  forks,  or  any  two  musical  instruments  are 
slightly  out  of  tune.  The  experiment  is  readily  made  with 
two  forks  which,  previously  in  tune,  are  put  out  of  tune  by 
loading  the  prong  of  one  with  a  small  piece  of  wax  and  thus 
flattening  its  note.  This  decrease  in  the  frequency  of  the 
vibrations  of  the  loaded  fork  makes  it  give  wave-lengths  in 
the  air  which  are  longer  than  those  given  by  the  unloaded 
fork. 

The  velocity  of  the  sound-waves  proceeding  from  each 
fork  is  the  same ;  but,  as  the  waves  are  of  different  lengths, 


FIG.  277.— Two  SERIES  OP  WAVES  ILLUSTRATING  BEATS  AND  INTERFERENCE. 

it  follows  that  at  a  certain  instant  the  condensation  in  two 
waves,  one  from  each  fork,  will  reach  the  ear  at  the  same 
moment.  Their  united  action  will  produce  a  sound  greater 
than  that  given  by  the  vibration  of  either  fork  alone,  and 
consequently  we  hear  a  louder  sound.  The  same  increase 
in  loudness  occurs  when  rarefactions  in  the  two  sounds  fall 
together  on  the  ear ;  but  just  between  these  periods  of  in- 
creased loudness  there  is  an  instant  when  the  sound  becomes 
very  feeble.  These  actions  give  to  the  sound  a  thumping 
character  called  beating. 

Fig.  277  explains  the  action  of  the  two  series  of  sound-waves  on 
each  other.  The  longer  waves  are  indicated  by  the  full  line ;  the 
shorter,  by  the  dotted  line.  These  waves  are  going  from  A  to  B.  An 
ear  at  B,  as  implied  in  the  figure,  is  receiving  a  condensed  half -wave 
from  one  source  of  sound,  and  a  rarefied  half  wave  from  the  other.  A 
very  feeble  sound  is  the  result ;  but  when  by  the  forward  motion  of  the 


REFLECTION  OF  SOUND.— ECHOES.  387 

waves  the  place  C  reaches  the  ear,  an  intense  sound  is  heard,  for  the 
two  half-waves  of  the  sounds  are  here  acting  together. 

Reflection  of  Sound — Like  light  and  radiant  heat, 
sound  is  reflected,  and  in  such  a  manner  as  to  make  the 
angle  of  reflection  equal  to  the  angle  of  incidence.  Spheri- 
cal mirrors  may  be  used  to  prove  the  principle.  Determine 
the  point  to  which  rays  of  light  converge  if  transmitted 
from  some  distant  source  of  illumination  to  a  mirror,  and 
reflected  therefrom.  Substitute  a  watch  for  the  light,  and 
hold  the  ear  at  the  point  of  convergence.  The  ticking  will 
be  heard  distinctly,  as  if  it  came  from  the  mirror,  instead  of 
the  watch.  The  wet  sails  of  ships,  when  bellied  by  the  wind, 
have  been  known  to  reflect,  to  ears  that  happened  to  be  at 
their  foci,  sounds  produced  at  great  distances. 

Apartments  in  which  reflections  are  produced  by  the  walls  are 
called  Whispering  Galleries.  The  dome  of  St.  Paul's,  London,  and 
that  of  the  national  Capitol,  furnish  examples  of  modern  whispering 
galleries.  One  of  the  most  remarkable  structures  of  this  kind  in 
ancient  times  was  the  Ear  of  Dionysius,  a  dungeon  so  called  from  the 
tyrant  of  Syracuse,  and  constructed  in  such  a  way  that  by  stationing 
himself  at  a  particular  point  he  could  overhear  the  unguarded  words 
of  his  prisoners. 

Echoes  are  merely  repetitions  of  sounds  by  reflection 
from  walls,  mountain-sides,  etc.  The  interval  that  must 
exist  between  the  sound  and  the  echo  may  easily  be  deter- 
mined if  the  distance  of  the  reflecting  surface  is  known. 
Thus,  for  a  distance  of  112  feet,  the  interval  at  62°  Fahr.  is 
equal  to  112x2  (the  entire  distance  traveled  by  the  direct 
and  reflected  sound)  divided  by  1,120,  the  velocity  of  sound 
at  that  temperature  of  the  air,  or  one  fifth  of  a  second. 

If  we  assume  that  five  syllables  can  be  pronounced  rapidly  in  a 
second  of  time,  then  it  is  evident  that  at  distances  less  than  112  feet 
there  can  be  no  distinct  echo,  even  of  a  single  syllable ;  the  reflected 
sound  mingles  with  the  direct  sound  of  the  speaker's  voice,  and  often 
confuses  his  utterance.  This  is  noticeable  under  stone  arches  and  in 
large  unfurnished  rooms.  The  echoes  of  a  room  are  modified  or  re- 
moved by  furniture  and  hangings ;  the  presence  of  an  audience  in  a 


388  SOUND. 

theatre  or  church  will  quench  sound-waves  and  thus  destroy  disagree- 
able reverberations,  for  sound  is  absorbed  like  light  and  heat.  The 
same  sound  may  be  repeated  more  than  once.  There  are  echoes  that 
repeat  a  syllable  twenty  and  even  thirty  times.  Mountain-regions 
afford  numerous  examples  of  multiple  echoes. 

The  property  possessed  by  long  tubes  of  conveying  sound  accurate- 
ly, is  due  to  repeated  reflection.  The  waves  of  sound,  being  reflected 
from  the  interior  of  the  tubes,  are  prevented  from  dispersing  as  in  the 
open  air  (see  page  380),  and  hence  are  but  slightly  diminished  in  loud- 
ness.  The  French  philosopher  Biot  found  that  he  could,  without  rais- 
ing his  voice,  converse  through  an  empty  pipe  three  fifths  of  a  mile 
long.  This  fact  has  been  turned  to  account  in  many  ways ;  the  common 
speaking-tube  is  familiar  to  all.  The  short  speaking-trumpet,  how- 
ever, does  not  act  by  reflection,  but  is  thought  to  owe  its  effect  partly 
to  resonance  and  partly  to  the  vibration  of  its  flaring  bell,  or  pavilion. 

Ear-Trumpets,  used  by  deaf  persons,  concentrate  and 
reflect  vibrations  to  the  interior  of  the  ear,  and  thus  render 
audible,  sounds  that  could  not  otherwise  be  heard. 

The  outer  part  of  the  ear  is  itself  of  such  a  shape  as  to  collect  the 
sound-waves  that  strike  it  and  reflect  them  to  the  membrane  within. 
To  enable  them  to  hear  more  distinctly,  we  often  see  persons  putting 
up  their  hands  behind  their  ears  so  as  to  form  a  concave  reflecting  sur- 
face. In  this  case,  the  hand  acts  somewhat  on  the  principle  of  the  ear- 
trumpet.  Instinct  teaches  animals  to  prick  up  their  ears  when  they 
want  to  catch  a  sound  more  clearly. 

Au'diphones  are  instruments  designed  to  collect  sound- 
waves and  transmit  the  vibrations  to  the  nerves  of  hearing 
through  the  bones  of  the  head.  They  sometimes  have  the 
form  of  a  fan  when  intended  for  ladies'  use,  and  are  pressed 
against  the  upper  teeth. 

Kefraction  is  a  property  of  sound.  To  prove  the  re- 
fraction of  sound  in  passing  from  one  conducting  medium 
to  another,  a  lens  12  to  18  inches  in  diameter  has  been  con- 
structed by  stretching  and  securely  fastening  thin  sheets  of 
India-rubber  on  a  wide  grooved  brass  ring,  and  inflating  the 
cavity  between  them  with  carbonic  acid  or  some  other  gas 
(see  No.  4,  page  370).  The  ticking  of  a  watch  suspended 
on  one  side  of  the  sound-lens  can  be  distinctly  heard  at  the 


DIFFRACTION  OF  SOUND.  389 

corresponding  focus  on  the  other,  while  almost  inaudible 
between  the  two  points.  This  could  not  be  so  unless  the 
sound-waves  from  the  watch,  in  passing  through  the  lens, 
were  bent  toward  its  axis. 

Sound  is  also  diffracted — that  is,  the  sound-wave  is 
bent  round  obstacles  in  its  path,  like  houses,  etc.,  which, 
however,  tend  to  "  shade  off  "  the  sound,  or  produce  an  ill- 
defined  sound- shadow.  The  diminished  intensity  in  the 
sound  of  a  railroad  train  as  it  enters  a  cutting  is  due  to  the 
fact  that  the  observer  is  in  such  a  shadow.  In  the  acoustic 
shadows  cast  by  buildings,  the  air-shocks  attendant  upon 
explosions  are  sensibly  modified. 

QUESTIONS.— Explain  the  nature  of  the  Transmission  of  Sound  by  means  of  the 
experiment  with  the  elastic  marbles.  By  what  are  the  sounds  ordinarily  heard 
transmitted  ?  Describe  compression  and  expansion  as  illustrated  in  a  glass 
tube.  Explain  condensation  and  rarefaction,  and  state  the  effect  of  each  on 
the  molecules  of  air.  Strike  your  tuning-fork  and  hold  it  near  your  cheek. 
Why  will  you  feel  little  puffs  of  air  ?  Now,  describe  accurately  a  sound-wave 
and  compare  it  with  a  water-wave.  Can  you  represent  a  sound-wave  on  the 
blackboard,  showing  how  the  condensation  and  rarefaction  constituting  it  are 
produced  ?  Construct  a  Crova's  disk,  mount  it  on  your  rotator,  and  illustrate 
the  nature  of  a  sound-wave,  and  the  manner  in  which  it  is  propagated.  De- 
scribe a  more  recent  experiment  which  aptly  illustrates  the  same  principle. 

What  is  meant  by  the  Interference  of  sound  ?  How  is  it  produced,  and  how  can 
it  be  rendered  apparent  ?  Why  are  there  four  places  of  silence  in  one  rotation 
of  a  vibrating  tuning-fork  ?  How  can  this  be  proved  with  the  fork,  and  a  com- 
mon tumbler  partly  closed  by  a  piece  of  glass  ?  Suggest  another  illustration 
of  the  interference  of  sonorous  vibrations.  What  are  beats  of  sound,  and  how 
are  they  produced  ?  Under  what  circumstances  may  the  phenomenon  be  ob- 
served ?  Draw  a  figure  explanatory  of  the  action  of  two  series  of  sound-waves 
on  each  other  in  producing  beats  and  interference. 

How  can  you  illustrate  the  Reflection  of  Sound  ?  Are  woven  fabrics  good  re- 
flectors ?  JVb,  because  they  are  pervious  to  sound.  What  are  whispering-gal- 
leries ?  Define  Echoes.  What  conditions  cause  single  echoes  ?  What,  multiple 
echoes?  On  what  does  the  number  of  syllables  repeated  depend  ?  When  is 
there  no  perceptible  echo  ?  Why  do  the  echoes  of  an  empty  building  disap- 
pear when  it  is  filled  with  people  ?  Explain  the  principle  of  the  speaking- 
tube  ;  of  the  speaking-trumpet ;  of  the  ear-trumpet ;  of  the  audiphone.  Why 
do  deaf  persons  place  their  hands  behind  their  ears  ?  Why  do  animals 
change  the  positions  of  their  ears  ?  Illustrate  Refraction  of  sound  ;  Diffrac- 
tion. In  arctic  regions,  persons  separated  by  more  than  a  mile  of  frozen  water 
have  conversed  with  ease  ;  can  you  suggest  a  reason  ?  In  such  cases,  the  air 
is  homogeneous,  and  offers  no  obstacle  to  the  free  transmission  of  sound-waves. 
Masses  of  unequally  heated  air  enfeeble  sound,  the  waves  being  broken  up  by 
refraction.  Why,  then,  can  sounds  often  be  heard  farther  at  night  than  by  day  ? 


390  SOUND. 


NATURE  OF  VIBRATIONS. 

Vibrations  of  Strings. — If  we  take  hold  of  a  stretched 

string  (A  B,  Fig.  278)  and  pull  it  out  of  the  straight  line 

A  B  to  C  and  then  let  it  go,  the  string  will  vibrate,  swinging 

D  from  0  to  D  and  from  D  to 

^---  -'  ~~— — ~,  C,  until  the  energy  of  its  mo- 

— . -—  tion  is  given   up  to  the  air, 

and  to  the  points  A  and  B 

FIG.  278.— VIBRATION  OF  STRING.          ,     ,  ,  .   ,    ..  . 

between  which  it  is  stretched. 

The  cause  of  this  vibration  is  the  successive  stretching  and 
relaxing  of  the  string;  for,  evidently,  when  it  is  pulled  to 
C,  the  length  A  B  has  become  A  C  -j-  C  B,  which  is  longer 
than  A  B. 

The  laws  which  govern  the  vibrations  of  strings,  wires, 
catgut,  etc.,  are  as  follows : 

1.  The  force  with  which  the  string  is  stretched  remain- 
ing the  same,  the  number  of  vibrations  in  a  given  time  are 
inversely  as  the  length  of   the  string.      Thus,  strings   of 
lengths  1,  2,  3,  4,  will  have  1,  -J,  £,  and  J  the  number  of 
vibrations  in  the  same  time ;  while  strings  of  lengths  J,  J,  J, 
will  vibrate  2,  3,  and  4  times  as  rapidly  as  the  string  of  the 
length  1. 

2.  In  strings  of   the  same  substance   and   length,  and 
stretched  with  the  same  force,  the  vibrations  will  be  inverse- 
ly as  their  diameters.     A  string  3  feet  long,  having  a  diam- 
eter of  -fa  inch,  will  vibrate  twice  as  many  times  in  a  second 
as  a  string  of  the  same  length  and  -fa  inch  in  diameter. 

3.  In  strings  of  the  same  length  and  of  the  same  diam- 
eter, the  number  of  vibrations  varies  as  the  square  root  of  the 
stretching  force.     Thus,  if  a  string  be  stretched  with  forces 
of  1,  4,  9,  16,  25,  the  number  of  its  vibrations  a  second  will 
be  as  1,  2,  3,  4,  5. 

4.  The  number  of  vibrations  will  be  inversely  as  the 
square  root  of  the  density ;  or,  what  is  the  same,  if  strings 


THE  SONOMETER. 


391 


equally  stretched  and  of  the  same  length  and  diameter  weigh 
respectively  1,  4,  9,  16,  25,  the  numbers  of  their  vibrations 
per  second  will  be  as  1,  £,  £,  J,  |,  of  the  string  having  the 
weight  of  1. 

The  Sonometer. — These  laws  have  been  determined 
by  experiments  with  the  Sonom'eter  (Fig.  279),  a  long  reso- 
nant-box, M  N,  having  two  bridges,  B  and  B'  near  its  ends. 
The  string,  gut,  or  wire,  is  attached  to  the  pin  P,  and 

stretched  be- 
tween the  two 
bridges  by 
passing  it  over 
the  pulley  H 
and  hanging 
to  its  end  the 
weight  W.  A 
scale  on  the 
top  of  the 
box  gives  the 

length  of  the  string  between  the  bridges.  On  vibrating 
the  string  by  plucking  it  at  its  center,  we  hear  a  definite 
musical  note,  which  rises  in  pitch  as  we  shorten  the  string 
by  sliding  the  bridge  B'  toward  B. 

If  we  move  B'  to  one  half  the  distance  B  B',  and  then  vibrate  the 
string,  we  hear  a  note  which  is  the  higher  octave  of  the  note  given  by 
the  whole  length  of  the  string.  As  we  shall  see  farther  on,  the  octave 
of  a  note  is  given  by  doubling  the  frequency  of  its  vibrations.  Thus, 
half  a  string  stretched  with  the  same  force  vibrates  twice  as  many 
times  a  second  as  the  whole  length.  If  we  sound  one  quarter  of  the 
string,  we  get  the  second  octave  above  that  given  by  its  whole  length. 
This  implies  that  when  one  quarter  of  the  string  is  vibrated,  it  makes 
four  times  as  many  vibrations  a  second  as  its  whole  length. 

The  second,  third,  and  fourth  laws,  are  proved  by  vibrating  wires 
having  different  diameters  and  stretched  with  various  weights,  or  hav- 
ing the  same  length  and  diameter  but  differing  in  weight. 

The    Harmonics  given  by  a  Vibrating  String. — 

Fig.  280  represents  a  thin  wire  stretched  between  bridges  A 


FIG.  279.— THE  SONOMETER. 


392  SOUND. 

and  B.  Place  the  beard  of  a  quill  at  n'  (in  the  top  figure), 
and  draw  a  violin-bow  across  the  wire  near  v.  Then  lift 
the  quill  from  the  wire.  We  now  see  the  wire  vibrating  as 

A  ,r  ,         V' B 

jf^11^         ~i^===£====^i ^^^k 


5 

FIG.  280.— THE  HARMONICS  OF  A  VIBRATING  STRING  OR  WIRE. 

if  formed  of  two  wires,  A  n'  and  n'  B.  At  n'  the  wire  is  at1 
rest,  or  nearly  so.  This  point  is  called  a  node.  At  v  and  v' 
is  the  greatest  excursion  or  bellying  of  the  string,  and  these 
places  are  called  the  venters  (Latin,  venter,  the  belly). 

The  two  parts  of  the  string  vibrate  with  a  seesaw  motion 
about  n\  so  that  v  and  v'  in  all  the  diagrams  of  Fig.  280  are 
always  moving  in  opposite  directions.  When  the  string 
vibrates  with  two  venters,  it  gives  out  the  higher  octave  of 
the  note  it  gave  when  it  had  only  one  venter. 

In  the  second,  third,  and  fourth  diagrams  of  Fig.  280,  with  3,  4, 
and  5  venters  respectively,  the  string  makes  3,  4,  and  5  times  the  num- 
ber of  vibrations  it  gave  when  it  vibrated 
with  only  one  venter.  If  the  number  of  vi- 
brations a  second  is  100  when  the  string 
vibrates  with  one  venter,  then  it  will  make 
200,  300,  400,  and  500  vibrations  when  it  has 
2,  3,  4,  and  5  venters. 

If  the  string  is  so  stretched  that  it  gives 
out  the  note  C  below  the  middle  C  of  the 
piano  (shown  in  the  bass  clef,  Fig.  281)  when 
it  vibrates  with  one  venter,  it  will  give  the  notes  numbered  2,  3,  4,  5,  6, 


VIBRATING  RODS. 


393 


Q\?/° 


7,  8  (shown  in  the  treble  clef),  when  it  vibrates  with  2,  3,  4,  5,  6,  7,  8 
venters.  These  notes  are  called  the  harmonics  of  the  note  in  the  bass 
clef,  and  are  given  by  2,  3,  4,  5,  6,  7,  8  times  the  number  of  vibrations 
given  by  the  C  in  the  bass.  Under  Analysis  of  Sounds,  we  shall  see 
that,  when  a  piano-string  is  struck  by  its  hammer,  all  these  harmonics 
except  the  seventh  are  present  in  its  sound. 

The  nature  of  vibrations  in  strings  may  be  effectively  studied  by 
means  of  the  zithern,  a  cheap  toy  consisting  of  a  sounding-board 
crossed  by  24  wire  strings  (see  No.  5,  page  370).  If  a  finger  be  placed 
on  the  center  of  one  of  the  strings  and  the  string  be  then  vibrated,  it 
will  yield  a  note  an  octave  higher  than  its  fundamental  note. 

The  Vibrations  of  Rods,  Tuning  -  Forks,  and 
Reeds. — A  rod,  clamped  in  a  vise,  is  shown  at  #,  #,  c,  d,  e, 
in  Fig.  282.  If  we  pull  the  rod  aside,  it  will  vibrate  till 
the  energy  of 
its  oscillations 
has  been  given 
to  the  air  and 
to  the  vise, 
and  has  been 
expended  part- 
ly in  heating 
the  rod  itself. 
These  vibra- 
tions have  the 
same  kind  of 

motion  as  that  of  a  swinging  pendulum ;  so  have  all  bodies, 
such  as  strings,  prongs  of  tuning-forks,  plates,  membranes, 
air  in  organ-pipes,  etc.,  which  give  forth  musical  sounds. 

If  we  place  a  soft  body  at  the  nodal  points  of  &,  c,  d,  e,  and  draw  a 
bow  across  the  rod  near  the  center  of  a  venter,  the  rod  will,  like  a 
string,  divide  itself  into  segments  of  vibration  with  nodes,  as  shown  in 
the  figures,  and  the  sounds  given  by  the  rod  when  it  has  these  nodes 
will  be  far  sharper  than  the  sound  given  when  the  rod  vibrated,  as 
shown  at  a. 

An  interesting  example  of  a  vibrating  rod  is  a  tuning-fork,  and  you 
here  have  the  analysis  of  its  motions  as  determined  by  experiments. 
Let  a  a  in  Fig.  283  represent  a  steel  bar  resting  on  cords  at  points 
26 


FIG.  282.— VIBRATING  RODS. 


394 


SOUND. 


Fia.  283. — FROM  THE  VIBRATING  ROD  TO 
THE  TUNING-FORK. 


shown  by  the  short,  perpendicular  dotted  lines.    These  dots  show  the 
position  of  the  nodal  lines  of  the  bar  when  it  is  struck  in  the  center. 

Now,  suppose  the  bar  bent  from 
the  straight  line  a  a  into  the 
curve  b  b.  The  two  nodal  lines 
exist,  but  approach  each  other. 
We  may  continue  to  bend  the 
rod,  causing  it  to  pass  through 
the  forms  c  and  d  to  e,  when  we 
have  the  tuning-fork. 

The  nodes,  during  these  suc- 
cessive bendings  of  the  rod,  have 
approached  each  other,  as  is 
shown  by  the  dotted  lines,  till  in 
the  tuning-fork  they  are  close  together  (p  and  q)  and  near  where  the 
prongs  of  the  fork  curve  inward.  The  fork  (Fig.  284)  now  vibrates  like 
the  unbent  rod  out  of  which  it  was  formed,  oscillatting  to  and  fro 
about  its  nodal  planes.  The  prongs  approach  each  other,  then  recede. 
When  they  approach,  the  foot  of  the  fork  is  pushed  down.  When 
they  recede,  the  foot  moves  up,  and  thus  the  fork  communicates  its 
vibrations  to  any  body  on  which  it  may  be  placed,  for  example,  to  a 
resonant-box  of  such  interior  dimensions  as  to  be  in  tune  with  the  fork. 

In  various  musical  instruments,  thin  plates  or  rods  are 
used.  Thus,  in  the  zylophone,  vibrating  wooden  rods,  and 
in  the  glass  harmonica,  strips  of  glass,  are  supported  at  their 
nodes  on  cords.  These  rods  or  glass  plates 
are  struck  with  a  light  wooden  hammer,  and 
give  sounds  of  life  and  brilliancy.  In  the 
common  music  -  box,  free  steel  tongues,  ar- 
ranged in  the  form  of  a  comb  and  made  fast 
at  one  end,  vibrate  at  the  other  when  lifted 
by  the  pins  of  a  revolving  cylinder,  yielding 
their  individual  notes.  In  the  vox-lmmana 
and  other  reed-pipes  of  the  organ,  in  the 
reed-organ,  and  in  the  clarionet,  reeds  or  thin 
plates  are  set  in  vibration  by  blasts  of  air. 
The  sounds  given  by  these  reeds  are  re-enforced  and  modi- 
fied by  their  setting  in  vibration  the  air  contained  in  pipes 
or  cavities  of  various  forms  and  sizes. 


FIG.  284.— VIBRA- 
TING FORK. 


VIBRATING  PLATES. 


395 


FIG.  285.— CHLADNI'S  FIGURES. 


Vibrations  of  Plates. — When  a  circular  plate  of  brass, 
glass,  or  other  elastic  substance,  is  fastened  at  its  center  to 
a  support,  and  a  violin-bow  is  drawn,  perpendicularly  to  the 
surface  of  the  plate,  across 
a  point  on  its  edge,  the 
plate  vibrates  and  gives 
forth  a  sound.  To  dis- 
cover how  such  a  plate  vi- 
brates, Chladni  spread  fine 
sand  over  it;  then,  on 
causing  it  to  vibrate,  he  saw  the  sand  at  first  violently  agitat- 
ed, but  in  a  few  moments  come  to  rest  in  narrow  wind-rows 
running  from  the  center  of  the  plate,  as  shown  in  Fig.  285. 

These  figures,  formed  by  sand  on  vibrating  plates,  are  hence  called 
Chladni's  figures ;  and-the  lines  of  rest,  nodal  lines.  The  plate  always 
divides  into  an  equal  number  of  vibrating  sectors.  This  is  explained 
by  the  well-established  fact  that,  in  adjacent  sectors,  it  always  vibrates 
with  opposite  directions  of  motion ;  the  line  of  sand  separating  any 

two  sectors  is  thus  a  nodal 
line,  where  there  is  very 
slight  motion,  or  abso- 
lutely none. 

Fig.  286  illustrates 
some  of  the  patterns  ob- 
tained by  vibrating  square 
plates.  Press  two  fingers 
against  the  edge  of  the 
plate  selected  for  the  ex- 
periment, at  points  where 
nodal  lines  are  to  appear, 
and  draw  the  bow  of  a 

violin  across  the  plate,  midway  between  the  points  held  at  rest  by  the 
fingers.    A  characteristic  figure  will  be  immediately  formed. 

Vibrations  of  Bells. — A  bell  may  be  considered  as  a 
plate  formed  into  a  spherical  surface.  Bells  have  nodal 
lines  or  planes  of  rest,  and  ventral  surfaces  where  the  vibra- 
tions are  greatest,  and  opposed  in  direction  on  opposite  sides 
of  the  nodal  lines.  Fig.  287  shows  how  a  bell  struck  by  the 


FIG.  286.— PATTERNS  ON  VIBRATING  SQUARE 
PLATES. 


396 


SOUND, 


clapper  at  #,  #,  c,  or  d,  will  have  at  these  points  the  center  of 
a  venter,  while  the  nodal  points  are  half-way  between  these 
points,  at  n>  n,  n,  n.  The  nodes  _JL_ 

and  venters  may  be  found  by  sus- 
pending to  a  string  a  small  ball  of 
ivory  or  of  metal.  When  the  ball 
touches  the  bell  at  #,  #,  c,  or  d,  it  a\ 
is  violently  repelled,  while  at  ft,  n 
n>  n,  it  is  very  slightly  agitated. 


FIG.  287. — VIBRATING  SEGMENTS 
AND  NODES  OF  A  BELL. 


Vibrations  ol  Columns  of 
Air. — Fig.  288  represents  a  glass 
tube,  T,  with  a  cork  in  it  which 
can  be  slid  to  various  positions. 
By  adjusting  the  cork  we  obtain  various  depths  of  air  in 
the  tube,  from  its  open  mouth  I  to  the  cork  c.  On  vibra- 
ting a  tuning-fork  over  the  mouth  of  the  tube,  while  the 
cork  is  gradually  slid  along  the  tube,  we  soon  learn  that, 

at  a  certain 
position  of 
the  cork,  the 
sound  of  the 

FIG.  288.— TUNING-FORK  AND  RESONANT  TUBE.  lOrk  IS  great- 

ly  increased 

in  loudness ;  and  that,  when  the  cork  is  removed  from 
this  position,  the  sound  rapidly  diminishes  in  inten- 
sity. If  the  diameter  of  the  tube  be  small  compared 
to  its  length,  we  shall  find  that  the  re-enforcing  of 
the  sounding-fork  reaches  its  maximum  when  the 
depth  of  the  column  of  air  measures  one  fourth  of  the 
wave-length  of  the  sound  given  by  the  fork. 

The  simple  formula  I  =  — ,  in  which  I  =  the  length  of  the  sound- 
wave, v  =  the  velocity  of  sound  at  the  temperature  of  the  air  in  the 
tube,  and  n  =  the  number  of  vibrations  a  second  made  by  the  fork, 
gives  us  the  means  of  determining  the  length  of  \  of  the  sound-wave 
propagated  by  the  fork.  If,  for  example,  the  fork  makes  256  vibrations 


ORGAN  PIPES.  397 

a  second,  and  the  temperature  of  the  air  is  65°  Fahr.,  then  I  =  —  or 
I  =  y??  =  4-38  feet,  or  52£  inches.    One  fourth  of  52£  inches  is  13i  - 

*w£)O 

the  length  of  the  column  of  air  in  the  tube  which  resounds  to  256  vi- 
brations a  second. 

The  explanation  of  the  above  fact  is  as  follows  :  The  prong  of  the 
fork  and  the  air  at  the  mouth  of  the  tube  must  vibrate  together ;  other- 
wise, there  will  be  interference  between  these  vibrations,  and  the  air  in 
the  tube  can  not  vibrate  with  the  fork  and  re-enforce  the  sound  the 
latter  originates.  We  have  previously  learned  that  the  fork,  in  going 
from  a  to  &  (Fig.  288),  makes  one  half  wave-length  in  the  air  before  it. 
This  may  be  represented  by  the  curve  bed,  above  the  line  b  d.  Now 
the  tube  T  must  be  as  long  as  from  b  to  c,  or  one  quarter  of  a  wave- 
length, so  that,  by  the  time  the  prong  of  the  fork  has  gone  from  a  to  b, 
and  is  just  beginning  its  back-swing  from  b  to  «,  the  half-wave  bed 
has  just  had  time  to  go  to  the  bottom  of  the  tube  T,  to  be  reflected 
back,  and  to  reach  the  prong  b  at  the  very  moment  of  its  back-swing. 
If  it  does  this,  then  the  end  of  this  reflected  wave  (shown  by  the  dotted 
curve  on  the  tube  T)  moves  backward  with  the  back-swing  of  the  prong 
&,  and  thus  the  air  at  the  mouth  of  the  tube  and  the  prong  of  the  fork 
swing  together,  and  the  sound  given  by  the  fork  is  strengthened. 

It  is  evident  that,  if  the  fork  makes  double  the  number 
of  vibrations  per  second  over  the  mouth  of  the  tube,  the 
column  of  air  in  the  tube  will  have  to  be  shortened  one  half 
in  order  that  it  may  resound ;  and,  if  the  fork  makes  half  the 
number  of  vibrations,  the  depth  of  air  in  the  tube  will  have 
to  be  doubled  to  re-enforce  the  sound  of  the  fork.  In  other 
words,  the  laws  ruling  these  phenomena  of  resonant  tubes 
are,  that  the  lengths  of  resonant  tubes  are  inversely  as  the 
number  of  vibrations  to  which  they  resound. 

Organ-Pipes  are  simply  resonant  tubes.  The  air  in 
such  pipes  is  set  in  vibration  by  vibrating  reeds,  or  by  air 
driven  through  a  mouth-piece  like  a  whistle's,  instead  of 
by  the  fork  as  in  our  experiments.  The  relation  between 
the  lengths  of  organ-pipes  and  the  numbers  of  vibrations  they 
give  is  approximately  the  same  as  in  the  case  of  resonant 
tubes,  viz.,  the  numbers  of  vibrations  a  second  given  by 
organ-pipes  of  similar  form  are  inversely  as  their  lengths. 


398  SOUND. 

If  in  the  equation  I  =  — ,  we  know  two  quantities,  we  can  deter- 
mine the  third ;  thus,  v  =  ln,  and  n=.~.     If  we  know  the  number  of 

vibrations  of  the  fork  per  second,  or  w,  and,  by  the  experiment  cited 
above,  obtain  the  length  of  the  wave,  or  /,  then  we  may  compute  the 
velocity  of  sound  in  air  at  65°  Fahr.  by  multiplying  n  by  L  In  the 
experiment  given,  n  equaled  256,  and  I  was  4-38,  and  256  x  4-38  =•  1,121. 
This  is  one  of  the  methods  which  has  been  used  to  obtain  the  velocity 
of  sound  in  various  gases. 

QUESTIONS.— State  the  laws  that  govern  the  Vibrations  of  Strings.  By  what  ex- 
periments have  these  laws  been  determined  ?  Describe  the  Sonometer.  Men- 
tion the  variety  of  notes  given  by  a  stretched  string.  What  will  be  the  effect  of 
halving  its  length  ?  Of  quartering  its  length  ?  What  is  a  node  ?  A  venter  ? 
Explain  what  is  meant  by  the  harmonics  of  a  vibrating  string.  They  are  "  the 
notes  corresponding  to  the  division  of  the  string  into  its  aliquot  parts."  What 
practical  use  may  be  made  of  the  zithern  in  this  connection  ? 

Draw  on  the  blackboard  a  series  of  figures  showing  how  a  rod  may  be  made  to 
divide  itself  into  segments  of  vibration,  like  a  string.  When  will  the  sound  be 
higher  pitched  ?  What  interesting  analysis  of  the  motions  of  the  tuning-fork 
can  you  give  ?  How  may  musical  tones  be  obtained  from  vibrating  rods,  plates, 
and  reeds  ?  Describe  the  principle  of  the  common  music-box.  What  are 
Chladnrs  figures,  and  how  are  they  produced  ?  Illustrate,  by  means  of  a  dia- 
gram, the  nodal  planes  and  ventral  surfaces  of  a  bell.  How  may  the  nodes  and 
venters  be  detected  ? 

What  is  meant  by  re-enforcing  the  sound  of  a  tuning-fork  ?  In  the  case  of  the 
fork  and  the  resonant  tube,  when  does  this  re-enforcement  reach  its  maximum  ? 
What  formula  affords  a  means  of  determining  the  length  of  sound-wave  propa- 
gated by  the  fork  ?  Define  a  wave  of  sound,  and  wave-length.  What  are 
organ-pipes  ?  What  relation  exists  between  their  lengths  and  vibrations  ? 


ELEMENTS  OF  SOUND.— MUSICAL  SCALE. 

Sounds   are  distinguished   by  Three   Qualities — 

pitch,  intensity  or  loudness,  and  timbre  (tim'ber). 

Pitch  is  that  quality  of  a  sound  by  which  we  distinguish 
its  position  in  the  musical  scale.  Thus,  we  speak  of  a  sound 
being  higher  or  lower  than  another.  Pitch  depends  on  the 
number  of  vibrations  made  by  the  sounding  body  in  a  cer- 
tain fixed  unit  of  time,  the  second.*  The  greater  the  num- 

*  In  this  country,  and  in  England  and  Germany,  a  vibration  is  understood  to 
be  a  movement  to  and  fro  of  the  vibrating  body.  In  France,  a  vibration  is  a 
movement  to  or  fro.  Hence  the  vibrations  given  by  French  writers  have  to  be 
halved  to  correspond  with  those  we  use. 


PITCH. 


399 


ber  of  vibrations,  the  higher  the  pitch.  Thus,  if  we  have 
three  sounds,  and  the  numbers  of  their  respective  vibrations 
are  to  each  other  as  1  :  2  :  4,  then  the  second  is  one  octave 
above  the  first,  and  the  third  is  an  octave  above  the  second 
and  two  octaves  above  the  first. 

The  ordinary  ear  is  sensitive  to  sounds  produced  by  vibrations 
varying  between  40  and  from  12,000  to  20,000  a  second.  If  vibrations 
fall  on  the  ear  fewer  in  num- 
ber than  40  to  the  second, 
they  do  not  blend  as  a 
musical  sound,  but  + 
give  a  sensation  re- 
sembling the  beats 
of  two  bass  organ- 
pipes  which  are 
considerably  out  of 
tune.  The  limit 
of  sensibility  to 
sounds  of  high  pitch 
varies  in  different 
persons.  The  results 
of  some  experiments 
made  by  the  author  in 
Washington  in  1875,  on 
the  hearing  of  Chief -Jus- 


tice Waite,  Prof.  Joseph 
Henry,  and  on  his  own 
ear,  are  as  follows  : — 


Limit  of  audition  of  acute  sounds  by- 
Prof.  Joseph  Henry,  12,300  vibrations. 
Alfred  M.  Mayer,        16,400 
Chief -Justice  Waite,  20,500       " 


FIG.  289.— THE  SIMPLE  SIREN  : 
RISE  OF  PITCH  WITH  NUM- 
BER OF  VIBRATIONS. 


As  some  persons  are  born  color-blind, 
so  there  are  others  who  are  deaf  to  certain 
notes.  Most  men  lose  the  power  of  appre- 
ciating very  high  notes  with  advancing  age,  and  sudden  shock  or  pro- 
longed mental  strain  has  been  known  seriously  to  impair  the  sensi- 
bility of  the  ear  to  sounds  of  different  pitch.  "We  have  seen  that  there 
are  many  objects  invisible  to  the  unaided  eye ;  so  there  may  be  sounds 
produced  by  insects  (implying  over  30,000  vibrations  to  the  second) 
that  are  wholly  inappreciable  by  the  human  ear. 


400 


SOUND. 


FIG.  290.— CARDBOARD  DISK. 


That  the  Pitch  rises  with  the  Number  of  Vibra- 
tions, is  proved  by  the  simple  apparatus  shown  in  Fig.  289. 
A  cardboard  disk  about  8-J-  inches  in  diameter  revolves  about 

its  center  on  the  rotator.  The 
disk  has  four  series  of  holes, 
each  series  equally  spaced  on 
its  respective  circle  (see  Fig. 
290).  On  the  first  or  inner  cir- 
cle are  24  holes,  on  the  second 
30,  on  the  third  36,  and  on  the 
fourth  48.  These  numbers  are 
to  each  other  as  24  :  30  :  36  : 
48,  or  as  4  :  5  :  6  :  8. 

If  we  rotate  the  cardboard 
disk  with  a  uniform  motion 
and  blow  through  a  glass  tube  placed  close  to  and  opposite 
the  inner  series  of  holes,  we  shall  produce  a  sound  having 
the  character  of  a  musical  note.  This  sound  is  caused  by 
vibrations  made  by  the  puffs  of  air  which  pass  through  the 
holes  as  they  successively  come  in  front  of  the  tube.  If  we 
pass  the  tube  from  the  first  to  the  second,  third,  and  fourth 
ring  of  holes,  the  sound  at  each  new  position  of  the  tube 
rises  in  pitch,  and  the  ear  distinguishes  in  the  sequence  of 
these  sounds  the  major  chord. 

In  other  words,  if  we  rotate  the  disk  so  rapidly  that  we  obtain 
from  the  first  series  of  holes  the  C  of  the  treble,  then  from  the  second, 
third,  and  fourth  series  of  holes  we  shall  have  the  sounds  of  E,  G',  and 
C'  of  the  octave  above  the  treble  C.  These  musical  intervals  are 
always  given  by  sounds  whose  vibrations  have  the  ratios  of  4  :  5  :  6  :  8. 

If  we  hold  the  tube  stationary  before  any  one  of  the  series  of 
holes,  we  shall  find  that  the  sound  rises  in  pitch  as  we  increase  the 
rapidity  of  rotation,  and  falls  as  we  slacken  the  speed  of  the  disk. 

The  Siren  (Fig.  291)  is  an  instrument  similar  in  action 
to  the  one  just  described,  and  much  used  to  determine  the 
pitch  of  sounds.  It  consists  of  a  metal  cylinder  into  whose 
base  air  is  blown.  The  top  of  the  cylinder  is  perforated 


THE  SIREN. 


401 


with  a  number  of  holes.  Just  over  this  top,  and  nearly 
touching  it,  rotates  a  metallic  disk  on  a  vertical  axis.  This 
disk  is  perforated  with  the  same  number  of  holes  as  are  in 
the  cylinder.  The  form  of  the  holes  is  shown  in  section  in 
the  figure.  They  do  not  pass  perpendicularly  through  the 
plates,  but  slope  contrariwise,  so  that  the  air  when  forced 
through  the  holes  in  the  top  of  the  cylinder  impinges  on 
one  side  of  the  holes  on  the  rotating  disk,  and  thus  blows  it 
round  in  a  definite  direction.  The  disk,  in  making  one 
revolution,  opens  and  shuts  the  holes  as  many  times  as  there 
are  holes  in  the  disk  and  cylinder,  and  hence  the  wind 
escapes  from  the  cylinder  in  successive  puffs,  the  frequency 
of  which  depends  on  the  velocity  of  rotation.  A  sound  is 
thus  produced  whose  pitch  rises  with  the  velocity  of  the 
disk.  The  vertical  axis  of  the  disk  has  a  screw  cut  on  it 
which  works  on  a  notched  wheel 
attached  to  a  dial  marking  the 
number  of  rotations. 

To  determine  the  pitch  of  a  sound 
with  this  instrument,  we  gradually  in- 
crease the  rotation  of  the  disk  until  the 
sound  given  out  approaches  the  pitch 
of  the  sounding  body  the  number  of 
whose  vibrations  we  would  determine. 
When  the  two  sounds  are  quite  near  in 
pitch,  the  ear  perceives  distinct  beats 
produced  by  their  joined  action  on  the 
air.  The  velocity  is  now  cautiously  in- 
creased by  regulating  the  blast  of  air 
through  the  instrument  until  the  beats 
just  disappear.  The  disk  is  then  al- 
lowed to  run  for  a  known  number  of 
seconds,  during  which  it  is  connected 
with  the  counter.  The  number  of  rota- 
tions is  thus  recorded.  If  this  number 
be  multiplied  by  "the  number  of  holes 

in  the  disk,  and  the  product  divided  by  the  number  of  seconds  the 
disk  was  connected  with  the  counter,  the  number  of  vibrations  per 
second  causing  the  sound  in  question  will  be  determined. 


402  SOUND. 

The  Intensity  of  a  sound  depends  on  the  energy  of  the 
air  vibrations  which  strike  the  ear,  and  therefore  on  the 
amplitude  or  extent  of  the  vibrations  of  the  sounding  body 
itself.  The  loudness  of  two  sounds  of  the  same  pitch  varies 
as  the  square  of  the  amplitude  of  the  air  vibrations.  After 
a  gong  has  been  struck,  the  effect  on  the  ear  gradually 
diminishes,  as  the  vibration  is  contracted  in  extent,  during 
the  return  of  the  vibrating  surface  to  rest. 

The  intensity  of  sound,  like  that  of  light,  has  been  found  to  vary 
inversely  as  the  square  of  the  distance.  Furthermore,  it  depends  on 
the  density  of  the  medium  in  which  the  sound  originates  and  is  prop- 
agated. The  denser  the  air  the  louder  the  sound,  because  the  quan- 
tity of  matter  impinging  on  the  drum-skin  is  greater.  Hence,  sounds 
produced  on  high  mountains,  where  the  air  is  rarefied,  are  correspond- 
ingly diminished  in  intensity.  We  have  seen  that  in  a  vacuum  there 
can  be  no  sound  ;  but  in  the  pneumatic  cais'son  employed  in  construct- 
ing bridge-piers  in  deep  water,  the  air  is  unnaturally  compressed,  so 
that  conversation  in  ordinary  tones  is  painful  to  the  ear. 

Timbre  is  a  quality  of  sound  which  affords  a  striking 
analogy  to  color  in  light.  We  may  have  a  red  and  an 
orange  light,  both  of  the  same  intensity ;  but  the  eye  dis- 
tinguishes one  from  the  other.  So  we  may  have  sounds  of 
the  same  intensity  and  pitch,  one  from  a  tuning-fork,  the 
other  from  a  violin,  piano,  clarionet,  or  the  human  voice. 
Yet  the  ear  distinguishes  these  sounds,  and  we  readily  name 
the  source  of  origin  in  each  case.  German  authors  have  an 
expressive  term  for  this  quality  of  sound.  What  we  call 
timbre  they  call  Klangfarle,  which  in  English  is  literally 
sound-color. 

The  different  timbres  of  sound  are  produced  by  min- 
gling various  simple  sounds,  just  as  any  color  may  be 
formed  by  mingling  various  proportions  of  red,  green,  and 
violet. 

A  Simple  Sound  is  one  in  which  the  ear  can  dis- 
tinguish only  one  sound  of  one  pitch.  Such  is  the  sound 
of  a  tuning-fork  vibrating  gently  on  its  resonant-box.  The 


SIMPLE  AND  COMPOSITE  SOUNDS.  403 

sound  of  a  closed  organ-pipe  is  also  very  nearly  a  simple 
sound.     All  simple  sounds  have  the  same  timbre. 

The  sound  of  a  piano-wire  is  an  example  of  a  Com- 
posite Sound,  for  it  is  composed  of  the  mingling  of  sev- 
eral simple  sounds.  Thus,  if  we  strike  the  treble  or  middle 
C  of  the  piano,  the  educated  ear  can  readily  detect  other 
and  higher  sounds  mingled  with  that  of  this  C.  The  latter 
sound  is,  however,  the  lowest  in  pitch  and  the  strongest  of 
the  component  sounds;  but  it  is  always  accompanied  by 
these  higher  sounds  whose  vibrations  bear  to  those  of  C  the 
ratios  of  1:2:3:4:5:6:7:8,  etc.  These  sounds  are 
called  the  harmonics,  or  overtones,  of  C  (see  page  391). 

If  we  designate  the  treble  C  by  Ca,  then  the  harmonics  mingled 
with  Ca  are  as  follows:  C3,  G3,  C4,  E4,  G4,  B(,4,  C6,  etc.  The  seventh 
harmonic,  or  B^4,  is  wanting  in  the  series,  because  the  hammers  of  the 
piano  strike  the  strings 'at  points  about  one  seventh  of  their  length; 
and  therefore  this  harmonic  can  not  sound,  for  the  blow  of  the  ham- 
mer makes  a  venter  at  the  point  it  strikes.  For  the  seventh  to  appear 
there  would  have  to  be  a  node  at  this  point.  The  seventh  is  thus 
purposely  obliterated  from  the  compound  sound,  for  it  is  not  in  har- 
mony with  the  other  harmonics. 

Analysis  of  the  Sound  of  a  Piano-String. — That 
these  harmonics  exist  in  the  sound  of  the  treble  C2  of  the 
piano,  is  easily  proved  by  the  following  interesting  experi- 
ment :  Depress  slowly  and  firmly  the  key  of  C3  on  the  piano. 
The  hammer  will  rise,  press  against  the  wire,  and  fall  from 
it ;  but  the  damper  of  this  string  will  remain  raised.  Now, 
strike  strongly  the  key  of  C3,  and  after  holding  it  for  an 
instant  stop  its  sound.  We  shall  hear  the  sound  of  C8  very 
distinctly,  showing  that  it  had  been  set  into  vibration  by 
the  vibration  of  C2,  and  that  08  must  therefore  exist  as  one 
of  the  component  sounds  of  C2.  In  like  manner  one  can 
show  that  G3,  C4,  E4,  G4,  GB,  etc.,  are  components  of  the 
compound  sound  of  the  wire  of  C2. 

Analysis  of  Complex  Sounds. — There  are  many  ways 
of  detecting  the  number  and  the  pitches  of  the  sounds  en- 


404  SOUND. 

tering  into  the  formation  of  any  complex  sound.  The 
sounds  used  in  music  are  all  complex,  for  a  simple  sound  is 
without  expression,  lacks  feeling  or  "  brilliancy."  We  have 
already  explained  one  method  of  analysis  in  which  we  have 
utilized  the  principle  of  co-vibration  (see  page  373).  There 
are  others  which  employ  this  same  principle. 

Suppose  we  wish  to  analyze  the  very  complex  sounds  given  by 
reed  organ-pipes.  Let  us  arrange  around  the  mouth  of  the  pipe 
tuning-forks  mounted  on  their  resonant-boxes.  The  lowest  sound 
rendered  by  the  pipe,  or  that  of  the  note  by  which  the  pipe  is  denoted 
in  the  musical  scale,  is  given  by  the  fork  lowest  in  pitch  in  the  series 
of  forks.  On  sounding  the  pipe,  this  fork  will  enter  into  vibration  ; 
and  on  stopping  the  sound  of  the  pipe,  the  fork  will  sing  out  clearly 
the  pipe's  lowest  or  fundamental  tone.  But  if  we  also  have  other 
forks  whose  vibrations  per  second  bear  to  those  given  by  the  first  fork 
the  ratios  of  2:3:4:5:6:7:8,  etc.,  they  will  also  sing  out  their  re- 
spective notes ;  and  when  we  stop  the  sound  of  the  pipe,  the  united 
sounds  or  chorus  of  the  forks  will  very  well  reproduce  the  peculiar 
timbre  of  the  reed  organ-pipe. 

We  thus  in  one  experiment  not  only  analyze  the  sound,  but  repro- 
duce it  by  the  chorus  of  its  components. 

Resonators  of  Helmholtz. — The  most  ready  way  of 
analyzing  a  complex  sound  is  that  suggested  by  Helmholtz. 

He  employed  a  series  of  hollow 
brass  or  glass  spheres,  each  hav- 
ing a  circular  opening  a  to  ad- 
,  mit  the  vibrations  of  the  outer 
air  to  the  air  in  the  interior  of 
the  sphere.  Opposite  this  open- 
ing is  a  nipple  £,  which  fits  in 
the  ear,  and  thus  conveys  the  vi- 

FIG.  292.— HELMHOLTZ  RESONATOR.  .  J 

orations  to  the  auditory  nerves. 

Each  resonator  is  made  of  such  dimensions  that  it  is  accu- 
rately in  tune  with  a  known  simple  sound,  and  the  note  of 
this  sound  is  marked  on  the  resonator.  When  this  note  is 
sounded  in  the  air,  the  air  in  the  resonator  co-vibrates  to 
it,  and  the  sound  of  the  note  is  heard  with  great  distinct- 


THE  MUSICAL  SCALE.  405 

ness,  to  the  exclusion  of  the  other  simple  sounds  that  may 
be  in  any  complex  sound. 

By  applying  one  resonator  after  another  to  the  ear,  we  analyze  a 
sound  into  its  components.  It  is  thus  found  that  the  analysis  of  the 
sound  of  the  piano-wire  is  the  same  that  was  reached  by  our  experi- 
ment ;  that  the  sounds  of  a  clarionet  are  formed  only  of  the  odd  har- 
monics, or  of  simple  sounds  in  the  ratios  of  1  :  3  :  5  :  7 ;  and  that  the 
sounds  of  a  flute  are  substantially  those  of  a  note  and  its  octave. 

The  Musical  Scale  is-  formed  of  sounds  differing  in 
pitch  by  definite  ratios  of  vibrations.  The  experiments  with 
the  simple  siren  (Fig.  289)  showed  that,  when  the  ratios  of 
the  frequencies  of  the  vibrations  of  four  notes  were  as 
4  :  5  :  6  :  8,  we  obtained  a  succession  of  sounds — so  that,  if 
the  sound  beginning  the  ratio,  or  4,  was  that  of  the  note  C, 
then  the  other  sounds  were  as  follows :  E,  G,  and  c,  of  the 
octave  above  C.  But  this  ratio  of  4  :  5  :  6  serves  to  form 
the  whole  of  the  natural  scale  of  music,  thus :  We  decide  on 
the  number  of  vibrations  a  second  which  shall  denote  the 
treble  C — 264,  for  instance.  Then— 

(1)  C  :  E  :  G  :  :  4  :  5  :  6  or  as  264  :  330  :  396 

(2)  G  :  B  :  d  :  :  4  :  5  :  6  or  as  396  :  495  :  594 

(3)  c  :  A  :  F  :  :  6  :  5  :  4  or  as  528  :  440  :  352 

By  arranging  these  results  in  the  order  of  the  notes,  we  have  the 
number  of  vibrations  corresponding  to  the  notes  contained  in  the  oc- 
tave of  the  treble,  viz. : 

Notes,  CDEFGABc* 

Vibrations,        264       297       330       352       396       440       495        528 

The  numbers  above  being  divisible  by  11,  we  may  reduce  the  ratios 
of  the  vibrations  to  their  simplest  expression : 

CDEFGABc 

24      :      27      :      30      :      32      :      36      :       40      :      45      :      48 

If  we  perforate  the  disk  of  the  siren  (Fig.  291)  with  holes  arranged 
in  8  circles — the  inner  circle  having  24  holes,  and  the  succeeding  circles 
27,  30,  32,  36,  40,  45,  and  48— then,  on  rotating  the  disk  so  that  we 
obtain  264  vibrations  a  second  by  blowing  through  the  circle  of  holes 

*  The  small  letter  indicates  the  octave  above  that  designated  by  the  corre- 
sponding capital. 


406  SOUND. 

nearest  its  center,  we  shall  obtain  all  the  notes  of  the  octave  by  blowing 
successively  through  the  circles  of  holes,  passing  from  the  inner  to  the 
outer  circle. 

This  natural  scale  is  the  only  one  which  gives  perfect 
harmony  of  chords.  It  is  the  scale  which  good  singers  use, 
and  which  the  accomplished  violinist  produces  from  his  in- 
strument. But  the  extensive  use  of  musical  instruments  with 
fixed  tones,  like  the  piano,  melodeon,  organ,  and  many  wind- 
instruments,  has  given  rise  to  a  scale  called  the  equal-tem- 
perament scale.  In  this  there  are  twelve  notes,  aud  the 
octave  is  divided  into  twelve  equal  intervals.  Each  of  these 
intervals  is  called  a  semitone,  and  two  intervals  form  a  tone. 

If  we  take  264  as  the  number  of  vibrations  of  the  C  of  the  treble, 
then  the  vibration  numbers  per  second  of  the  12  notes  of  the  octave 
will  be  as  follows : 

0     CJ      D      Djj      E       F      F|f      G      Gjf      A      Ajf      B 

264  280-  296+  314-  333-  352+  373+  395+  419+  444-  470+  498  + 

0      D   Efc   E   F       G   A|,   A   B[>   B 

264       297   317-   330   852        396   422+   440   469+   496 

The  ratios  above  are  given  to  the  nearest  integer.  Where  the 
note  is  slightly  sharper,  +  is  placed  after  it ;  where  slightly  flatter,  — 
follows  it.  For  comparison,  the  ratios  of  vibration-numbers  of  the 
perfect  or  natural  scale  are  written  under  those  of  the  equal-tempera- 
ment scale. 

The  intervals  of  the  equal  temperament  scale  are  so  near  to  perfec- 
tion that,  when  a  succession  of  notes  is  sounded  in  a  melody  on  the 
piano  or  organ,  only  the  cultivated  ear  of  a  musician  can  detect  the 
departure  from  accurate  tuning  in  these  instruments ;  but,  when  accom- 
plished singers  are  accompanied  either  by  piano  or  organ,  the  want  of 
harmony  between  the  voice  and  these  instruments  is  apparent.  This 
departure  from  accuracy  is  at  once  brought  out  when  chords  are  sound- 
ed on  the  piano  or  organ. 

The  best  violinists  play  the  natural  scale,  as  was  shown  by  Helm- 
holtz.  He  accurately  tuned  a  harmonium,  or  reed-organ,  to  the  natu- 
ral scale,  and  Joachim  (yo'a-kini),  the  eminent  violinist,  having  brought 
his  violin  to  the  pitch  corresponding  to  that  of  the  harmonium,  accom- 
panied the  latter  instrument.  It  was  found  that  the  intervals  played 
by  Joachim  were  those  of  the  natural  scale. 


THE  VOCAL   ORGANS.  407 

QUESTIONS.— Name  the  three  qualities  that  distinguish  sounds.  Define  Pitch.  On 
what  does  it  depend  ?  Between  what  limits  of  vibration  is  the  ear  sensitive  to 
sound  ?  Explain  the  sensation  produced  by  vibrations  fewer  in  number  than  40 
to  the  second.  Give  some  idea  of  the  limit  of  audition  of  acute  sounds.  State 
the  effect  of  age  on  the  power  of  appreciating  high  notes  ;  the  general  effect  of 
shock  and  mental  strain.  Prove  that  the  pitch  rises  with  the  number  of  vibra- 
tions, drawing  a  diagram  of  a  simple  Siren  to  illustrate  your  arguments.  De- 
scribe the  method  of  determining  the  pitch  of  a  sound  with  the  siren. 

On  what  does  the  Intensity  of  a  sound  depend  ?  Can  the  loudness  of  sounds  of 
the  same  pitch  vary  ?  How  ?  What  relation  exists  between  intensity  and  dis- 
tance ?  Between  intensity  and  density  of  medium  ?  What  can  you  say  of  the 
intensity  of  sounds  on  high  mountains  ?  Explain  Timbre,  and  the  analogy  to 
color.  What  is  a  simple  sound  ?  A  composite  sound  ?  Explain  the  harmonics. 
Analyze  the  sound  of  a  piano-string.  Do  the  harmonics  exist  in  the  sound  of  the 
treble  C2  ?  How  may  the  number  and  pitches  of  the  sounds  forming  any  com- 
plex sound  be  determined  ?  Describe  the  Resonators  of  Helmholtz. 

Of  what  is  the  Musical  Scale  formed  ?  What  ratio  forms  the  natural  scale  of 
music  ?  Reduce  the  ratios  of  the  vibrations  to  their  simplest  expression.  How 
can  we  obtain  all  the  notes  of  the  octave  with  the  simple  siren  ?  Explain  the 
equal-temperament  scale. 


THE  VOCAL  ORGANS  AND   THE  HUMAN  VOICE. 

How  we  Speak  and  Sing. — The  little  musical  instru- 
ment with  which  we  speak  and  sing  is  formed  of  two  flexible 
membranes  stretched  side  by  side  across  a  short  tubular  box 
placed  on  the  top  of  the  windpipe.  This  box,  the  lar'ynx, 
is  made  of  plates  of  cartilage,  movable  on  one  another,  and 
bound  together  with  muscles  and  membranes. 

The  top  of  the  windpipe  is  formed  of  a  large  ring  of  cartilage,  called 
the  cricoid  (wing-shaped)  cartilage.  Jointed  to  this  is  a  broad  plate, 
called  the  thyroid  (shield-shaped)  cartilage,  which  has  the  form  of  the 
letter  V.  The  angle  of  the  V  points  toward  the  front  of  the  throat, 
and  is  familiarly  known  as  the  "  Adam's  apple."  On  the  back  of  tho 
upper  edge  of  the  cricoid  ring  are  jointed  two  small,  pointed  cartilages, 
known  as  the  aryt'enoid  (funnel-shaped)  cartilages.  Stretching  from 
them  to  the  inner  surface  of  the  thyroid  are  two  yellowish-white  elastic 
membranes,  the  so-called  vocal  cords. 

When  the  point  of  the  thyroid  is  not  pulled  down,  these  cords  are 
loose,  and  the  breath  from  the  windpipe  passes  freely  between  them, 
and  does  not  make  them  vibrate  (see  B,  Fig.  293).  But,  when  the  peak 
of  the  thyroid  is  pulled  down  by  its  muscles,  the  vocal  cords  are 
stretched.  At  the  same  time  the  arytenoid  cartilages  move  nearer 


408 


SOUND. 


together,  and  the  thin,  sharply-cut  edges  of  the  cords  themselves  are 
brought  parallel  and  quite  close  to  each  other,  as  is  shown  in  A. 


FIG.  293.— HUMAN  LARYNX  AND  VOCAL  CORDS. 

A  and  B,  views  of  the  human  larynx  from  above  as  actually  seen  by  the  aid 
of  the  instrument  called  the  laryngoscope  ;  A,  in  the  condition  when  voice  is  be- 
ing produced ;  B,  at  rest,  when  no  voice  is  produced  ;  e,  epiglottis  (foreshort- 
ened) ;  cv,  the  vocal  cords  ;  «,  elevation  caused  by  the  arytenoid  cartilages  ;  Z, 
root  of  the  tongue. 

If  air  from  the  lungs  is  now  forced  through  the  narrow  slit  between 
the  cords  (called  the  glottis)  they  vibrate  like  the  tongue  of  a  reed-pipe, 
and  produce  the  sounds  of  the  voice.  The  almost  infinite  variety  of 
sounds  that  one  can  evoke  from  this  instrument  is  the  result  of  various 
degrees  of  stretching  (tension)  of  the  vocal  cords,  combined  with  the 
movements  of  the  mouth,  lips,  and  tongue. 

The  shorter  and  more  tense  the  cords,  the  higher  will  be  the  pitch. 
The  vocal  cords  being  shorter  in  women  and  boys  than  in  men,  their 


FIG.  294.— APPEARANCE  OF  THE  VOCAL  CORDS  IN  THE  PRODUCTION  OP  THE 
FALSETTO  VOICE. 

voices  are  sharper,  or  higher-pitched,  than  those  of  the  latter.  When  a 
boy  reaches  the  age  of  fourteen  or  fifteen,  his  larynx  develops  rapidly, 
the  cords  lengthen,  and  his  voice  "breaks,"  falling  usually  an  octave 


THE  HUMAN  VOICE.— SPEECH.  409 

in  pitch.  In  exceptional  cases,  the  development  of  the  larynx  is 
checked,  so  that  the  adult  man  is  able  to  sing  soprano  parts.  Some 
have  the  power  of  shortening  at  will  the  vibrating  parts  of  the  cords, 
and  so  producing  falsetto  notes  of  different  pitch.  In  such  cases,  the 
cords  may  be  brought  closer  together  posteriorly,  or  both  in  their 
posterior  and  anterior  portions,  as  shown  in  Fig.  294. 

Disorders  of  the  Voice. — The  production  of  the  sim- 
plest tone  implies  freedom  of  the  vocal  cords  to  approach 
each  other ;  and  complicated  vocal  effects  involve  the  action 
of  nearly  100  muscles  in  producing  and  driving  the  current 
of  air,  regulating  the  tension  of  the  cords,  and  changing 
the  size  and  form  of  the  oral  cavity.  Hence  the  power  and 
quality  of  the  voice  are  extremely  subject  to  changes.  All 
depressing  diseases  weaken  the  voice ;  any  interference  with 
the  perfect  or  regular  approximation  of  the  cords,  as  in  the 
case  of  a  cold  or  straining  of  the  voice,  causes  hoarseness  or 
huskiness ;  and  certain  forms  of  paralysis  and  painful  affec- 
tions of  the  throat,  in  which  the  cords  can  not  meet,  are 
marked  by  aphonia,  or  complete  loss  of  musical  tone.  The 
human  voice  is  also  peculiarly  susceptible  to  emotional  in- 
fluences ;  hence  the  hoarseness  or  tremulous  utterance  of 
passion,  the  speechlessness  of  fear,  etc. 

Speech  is  voice  modified  and  modulated  by  the  move- 
ments of  the  lips,  the  tongue,  and  the  parts  of  the  cavity 
of  the  mouth.  The  oral  cavity  is  made  larger  or  smaller, 
longer  or  shorter,  and  thus,  resounding  to  some  lower  01 
higher  harmonics  of  the  voice,  it  makes  the  others  feebly 
heard. 

All  the  vowel-sounds  are  formed  by  a  steady  voice,  modi- 
fied by  the  resonance  of  the  different  sizes  and  shapes  given 
to  the  cavity  of  the  mouth.  The  consonants  are  made  by 
obstructions  placed  at  the  beginning  or  end  of  the  oral 
sounds,  by  the  movements  of  the  tongue  and  lips. 

The  lower  animals  have  voice,  but  are  without  the  power 
of  significant   articulate   speech.      The   utterances   of  the 
parrot  are  mechanical,  not  intelligent. 
27 


4:10 


SOUND. 


Koenig's  Manometric  Flames. — Many  interesting 
and  instructive  experiments  with  the  human  voice  may  be 
made  by  means  of  a  simple  apparatus  invented  by  Koenig, 
of  Paris.  Fig.  295  shows  it  in  a  simple  form.  An  upright 


FIG.  295.— ANALYSIS  OP  SOUNDS  WITH  MANOMETRIC  FLAMES. 

piece  of  wood,  A,  noted  also  in  the  corner  of  the  figure, 
has  a  hole  bored  in  it  by  a  center-bit.  This  hole  does  not 
pass  entirely  through  the  piece  of  wood,  but  another  and 
smaller  hole  is  bored  in  the  center  of  the  one  just  formed. 
Similar  holes  are  bored  in  the  block  B,  which  has  also  an- 


MANOMETRIC  FLAMES. 

other  hole  bored  obliquely  into  the  cavity  formed  by  the 
center-bit.  A  piece  of  very  thin  paper,  gold-beater's  skin, 
or  India-rubber,  is  placed  over  the  large  hole  of  the  block  A 
so  as  to  cover  it,  and  is  cemented  to  the  block  by  glue  or 
mucilage.  The  block  B  is  then  placed  on  A,  as  shown,  and 
these  two  pieces  of  wood  are  glued  together. 

We  have  now  a  box  separated  into  two  compartments  by  the  sheet 
of  rubber.  Into  one  of  these  compartments  gas  is  led  by  a  rubber 
tube,  as  shown.  This  gas  issues  from  the  box  by  the  tube  D,  whose 
upper  end  is  drawn  out  into  a  burner.  The  gas  is  lighted  at  F,  and 
then  lowered  till  it  burns  with  a  small  bright  flame.  - 

Into  the  other  compartment  of  the  box  enters  a  large  glass  tube, 
E,  to  which  is  attached  a  rubber  tube  having  at  its  other  end  a  cone 
made  of  cardboard.  A  flat  piece  of  wood  is  cut  out,  as  shown  at  M, 
and  by  means  of  rubber  bands  two  pieces  of  mirror  are  fastened  to 
the  faces  of  the  board.  The  upright  rod  of  the  mirror  is  rotated  in  a 
conical  cavity  formed  on  the  block  K,  which  rests  on  the  brick  L. 

When  you  sing  into  the  cone  while  the  mirror  is  twirled  between 
the  fingers,  the  flame  viewed  in  the  mirror  presents  the  appearance  of 
a  band  of  light  with  its  upper  edge  cut  into  teeth  like  those  of  a  saw. 
This  shows  that  the  flame  is  vibrated  by  the  action  of  the  voice  on  the 
membrane,  which  divides  the  box  into  halves.  On  one  side  of  the 
membrane  is  the  flowing  gas  ;  on  the  other,  the  air  in  a  state  of  vibra- 
tion. 

When  the  condensed  half  of  a  sound-wave  falls  on  this  mem- 
brane, the  latter  is  forced  into  the  compartment  in  which  is  the  gas, 
and  the  gas  is  driven  out  of  the  tube  D  in  a  short  puff,  causing  the 
flame  suddenly  to  rise  in  height.  At  the  next  instant  the  membrane 
goes  in  the  opposite  direction  under  the  action  of  the  rarefied  half- 
wave,  and  the  flame  suddenly  falls.  These  motions  succeed  each  other 
several  hundred  times  in  a  second. 

When  the  mirror  is  revolved  and  no  sound-vibrations  enter  the 
cone,  the  reflection  from  the  mirror  draws  the  light  of  the  flame  into 
a  brilliant  band  or  ribbon ;  but  on  singing  into  the  cone,  you  will  see 
the  flame  vibrate,  and  the  upper  edge  of  the  band  become  serrated. 
Each  tooth  shows  a  vibration  of  the  membrane,  which  thus  faithfully 
gives  an  account  of  its  motions  on  the  flame  reflected  from  the  mirror. 
As  you  change  the  note  of  your  voice,  the  appearance  of  the  flame  will 
change.  If  the  mirror  is  revolved  regularly,  then,  as  the  pitch  of  the 
voice  rises,  the  number  of  teeth  increases  in  the  band  of  light. 


SOUND. 


EXPERIMENTS. — The  following  experiments  give  much  information  about  the 
sounds  of  the  voice  : 

Sing  into  the  cone  the  sound  of  oo  in  pool.    After  a  few  trials,  you  will  ob- 

tain   a   simple   sound,  and  the 

flame  will  appear  as  in  Fig.  296  A. 
While  twirling  the  mirror 
with  the  same  velocity  it  had 
during  the  preceding  experi- 
ment, lower  your  voice  to  the 
octave  below  the  oo  just  sung, 
and  the  flame  will  appear  as 
in  Fig.  296  J5,  with  one  half  the 
number  of  serrations,  because 
the  lower  octave  of  a  note  is 
given  by  one  half  the  number 
of  vibrations. 

Sing  the  song  o  on  the  note, 


and  you  get  Fig.  296  C.  This  is 
evidently  not  the  figure  that  a 
simple  sound  gives.  It  is  formed 
of  alternating  large  and  small 
teeth.  The  larger  teeth  are  made 
by  every  alternate  vibration  of 
the  octave  of  the  higher  sound 
D  coinciding  with  a  vibration  of 
the  octave  below.  Such  is  the 
character  of  the  generality  of 
sounds  given  by  a  flute. 
FIG.  296.  Fig.  296  D  appears  on  the 

mirror  when  we  sing  the  English 

vowel  a  on  the  note  /  of  the  octave  above  the  treble.  This  sound  is  made  up  of 
two  simple  vibrations  combined.  One  of  these  alone  would  make  the  long 
tongues  of  flame ;  but  with  this  simple  vibration  exists  another  of  three  times 
its  frequency — that  is,  the  latter  is  the  third  harmonic  of  the  lower  sound. 


QUESTIONS.— Describe  in  detail  the  human  larynx  with  its  appendages,  and  the 
action  of  the  vocal  cords  in  producing  the  Voice.  What  causes  a  high-pitched 
voice  ?  A  low-pitched  voice  ?  Explain  the  difference  between  the  voice  of  a 
woman  and  that  of  a  man ;  the  production  of  falsetto  tones.  Illustrate  the 
sensibility  of  the  voice  to  disease,  strain,  and  emotional  influences.  What  is 
Speech  ?  Explain  the  production  of  vowels  and  consonants. 

Describe  Koenig's  manometric  flames,  and  state  what  is  to  be  learned  from  them. 
Enumerate  certain  experiments  which  give  much  information  in  regard  to  the 
sounds  of  the  voice. 


THE   PHONOGRAPH.  413 


THE  TALKING-MACHINES.— HARMONY  AND  DISCORD. 

The  Vocal  Cords  and  the  Larynx,  with  the  cavities 
of  the  mouth  and  nose,  form,  as  has  been  shown,  an  instru- 
ment similar  to  a  reed-organ  pipe.  A  vox-humana  pipe  can 
be  made  to  articulate  some  simple  words  like  papa'  and 
mamma!.  These  experiments  are  made  by  forming  a  cavity 
between  the  two  hands,  and  then  opening  and  shutting  this 
cavity  at  the  proper  times,  while  the  open  mouth  of  the  pipe 
is  between  the  hands.  Reed-pipes,  with  a  little  practice,  can 
also  be  made  to  say  "  Amen,"  "  Go  away,"  and  several  other 
simple  combinations. 

Faber's  Talking-Machine. — The  experiments  with 
the  reed-organ  pipe  show  the  principles  followed  by  Faber, 
of  Vienna,  in  the  construction  of  his  celebrated  talking- 
machine.  A  vibrating  ivory  reed,  of  variable  pitch,  forms 
the  vocal  cords.  There  is  a  mouth-cavity,  whose  shape  and 
size  can  be  rapidly  changed  by  depressing  the  keys  on  a 
key-board.  Rubber  tongue  and  lips  make  the  consonants. 
A  little  windmill  turning  in  the  throat  rolls  the  r,  and  a 
tube  is  attached  to  the  nose  of  the  machine  when  it  is  de- 
sired to  produce  the  nasal  sounds  of  French. 

Edison's  Talking  Phonograph. — From  this  descrip- 
tion it  is  evident  that  Faber  worked  at  the  source  of  articu- 
late sound,  and  built  up  an  artificial  organ  of  speech,  whose 
parts  as  nearly  as  possible  perform  the  same  functions  as 
corresponding  organs  in  our  vocal  apparatus.  Faber  at- 
tacked the  problem  on  its  anatomical  side.  Edison,  how- 
ever, considering  the  vibrations  as  already  produced,  it  mat- 
ters not  how,  makes  them  impress  themselves  on  a  sheet  of 
metallic  foil  or  on  a  hard  wax  composition,  and  then  repro- 
duces from  these  impressions  the  sonorous  vibrations  which 
caused  them. 


414 


SOUND. 


Figs.  297  and  298  will  render  intelligible  the  construction  of  Edi- 
son's invention.  A  cylinder,  C,  turns  on  an  axle  which  passes  through 
the  two  standards  A  and  B.  On  one  end  of  this  axle  is  the  crank  D  ; 
on  the  other,  the  heavy  fly-wheel  E.  The  portion  of  the  axle  to  the 


FiGr.  297.— EDISON'S  TALKING  PHONOGRAPH. 


right  of  the  cylinder  has  a  screw-thread  cut  on  it,  which,  working  on  a 
nut  in  A,  causes  the  cylinder  to  move  laterally  when  the  crank  is 
turned.  On  the  surface  of  the  cylinder  is  scored  a  screw-thread  similar 
to  that  on  its  axle.  F  (shown  in  detail  in  Fig.  298)  holds  a  plate  of 
iron  about  ^  of  an  inch  thick.  This  plate  can  be  moved  toward  and 
from  the  cylinder  by  pushing  on  or  pulling  out  the  lever  H  Of,  which 
turns  in  a  horizontal  plane  about  the  pin  I. 

The  under  surface  of  this  thin  iron  plate  (A,  Fig.  298)  presses 
against  short  pieces  of  rubber  tubing, 
which  lie  between  the  plate  and  a 
spring  attached  to  E.  The  end  of  this 
spring  carries  a  rounded  steel  point,  P, 
which,  when  brought  up  to  the  cylin- 
der by  the  motion  of  the  handle,  H,  en- 
ters slightly  into  the  grooves  scored  on 
the  cylinder,  C.  The  distance  of  the 
point  P  from  the  cylinder  is  regulated 
by  a  set-screw,  S,  against  which  abuts 
the  lever  H  G.  Over  the  iron  plate  A 
is  a  disk  of  vulcanite,  B  B,  with  a  hole 
in  its  center.  The  under  side  of  this 
disk  nearly  touches  the  plate  A.  Its 
upper  surface  is  cut  into  a  shallow,  fun- 
nel-shaped cavity,  leading  to  the  opening  in  its  center. 

To  operate  this  machine,  we  first  neatly  coat  the  cylinder  with  a 


FIG.  298.— PRINCIPLE  OP  PHONO- 
GRAPH. 


EDISON'S  PHONOGRAPH.  415 

sheet  of  foil,  so  that  if  we  turn  the  cylinder  it  will  make  a  depressed 
line  or  furrow  where  the  foil  covers  it.  The  mouth  is  now  placed 
close  to  the  opening  in  the  vulcanite  disk,  B  B,  and  the  metal  plate  is 
talked  to  while  the  cylinder  is  revolved  with  a  uniform  motion.  The 
thin  iron  plate  vibrates  to  the  voice  and  the  point  P  indents  the  foil, 
impressing  on  it  the  varying  numbers,  amplitudes,  etc.,  of  the  vibra- 
tions. If  the  vibrations  given  to  the  plate  A  are  those  of  simple 
sounds,  then  they  are  of  a  uniform  regular  character,  and  the  point  P 
indents  the  foil  with  regular  undulating  depressions.  If  the  vibra- 
tions are  those  of  complex  and  irregular  sounds  (like  the  sounds  of  the 
voice  in  speaking),  then  the  depressions  made  on  the  foil  are  similarly 
complex  and  irregular.  Thus  the  yielding  and  inelastic  foil  receives 
and  retains  the  mechanical  impressions  of  these  vibrations. 

A  permanent  impression  having  been  thus  made,  we  now  obtain 
from  these  impressions  the  aerial  vibrations  which  made  them  in  the 
following  manner  :  The  plate  A  with  its  point  P  is  moved  away  from 
the  cylinder  by  pulling  toward  the  experimenter  the  lever  H  G.  Then 
the  motion  of  the  cylinder  is  reversed  till  there  is  brought  opposite  to 
the  point  P  the  beginning  of  the  impressions  it  made  on  the  foil.  The 
point  attached  to  the  plate  A  is  now  brought  up  to  the  cylinder,  and  a 
large  cone  of  paper  or  of  tin  is  placed  against  B  B  to  re-enforce  the 
sound.  The  crank  is  then  steadily  turned.  The  elevations  and  de- 
pressions made  by  the  point  P  now  pass  under  this  point,  and  in  doing 
so  cause  it  and  the  iron  plate  to  make  over  again  the  precise  vibra- 
tions which  animated  them  under  the  action  of  the  voice.  The  conse- 
quence of  this  is,  that  the  iron  plate  gives  out  the  vibrations  which 
previously  fell  upon  it,  and  thus  repeats  what  was  said  to  it  in  the 
very  tones  of  the  speaker. 

Persons  traveling  in  distant  lands  may  now,  after 
"  speaking  into  "  their  phonographs,  send  the  cylinders  of 
wax  composition  by  mail  to  their  friends,  who  have  simply 
to  revolve  these  cylinders  in  similar  instruments,  and  listen 
to  the  messages  they  utter.  The  phonograph  is  also  used 
by  physicians  to  record  the  sounds  made  in  coughing. 
Peculiar  coughs  characterize  different  diseases  and  different 
stages  of  the  same  malady,  and  these  may  now  be  preserved 
for  comparison  and  leisurely  study. 

The  Improved  Phonograph. — Edison  has  recently 
greatly  improved  his  phonograph,  and  has  given  us  a  ma- 


416  SOUND. 

chine  which  reproduces  speech  and  musical  tones  with  all 
their  delicate  shades  of  expression  and  modulation.  He  has 
in  this  later  machine  replaced  the  metallic  foil  by  a  cylinder 
of  a  hard  wax  composition,  which  can  be  placed  on  and 
taken  off  the  machine.  This  cylinder  is  turned  by  an  elec- 
tric motor,  regulated  by  a  governor.  For  the  iron  plate 
which  received  and  reproduced  the  vibrations,  he  has  sub- 
stituted one  of  thin  glass ;  and  instead  of  the  point  which 
indented  the  tin-foil,  he  now  uses  a  delicate  chisel  which 
cuts  out  the  wax  on  the  cylinder,  and  thus  engraves  in  the 
wax  the  most  delicate  variations  of  vibratory  motion  of  the 
thin  glass  plate. 

Harmony  and  Discord. — If  flashes  of  light  succeed- 
ing one  another  a  few  times  in  a  second  enter  the  eye,  a 
painful  sensation  is  caused ;  but,  if  the  number  of  flashes  a 
second  is  increased  till  they  exceed  10  or  20,  a  steady  light 
is  perceived  and  the  disagreeable  sensation  vanishes.  The 
reason  of  this  is,  that  the  impression  of  the  flash  of  light 
remains  as  light  on  the  eye  about  -fa  of  a  second,  and,  if 
another  flash  follows  before  the  impression  of  the  former 
has  disappeared,  the  two  sensations  blend  and  we  have  a 
continuous  sensation.  On  this  fact  Helmholtz  construct- 
ed his  theory  of  harmony  and  discord,  by  showing  that 
the  same  effect  was  produced  by  what  we  may  call  flashes 
or  beats  of  sound  (see  page  386).  He  did  not,  it  is  true, 
determine  experimentally  the  number  of  beats  in  a  second 
required  by  various  sounds  to  blend  into  a  continuous  sen- 
sation. This  was  first  done  by  Prof.  Mayer,  who  found 
out  the  facts  by  experiments  with  disks  perforated  with 
various  sizes  and  numbers  of  holes,  which  admitted  and 
shut  off  the  sound,  and  thus  produced  flashes  of  sound  on 
the  ear. 

Thus  it  was  found  that  the  duration  of  the  sensation  of 
a  sound  depends  on  the  pitch  of  the  sound,  and  that  the 
higher  the  pitch  the  less  the  duration  of  the  sonorous  sen- 


HARMONY  AND  DISCORD. 


417 


sation.     The  following  table  gives  the  results  of  these  ex- 
periments : — 


N 

V 

B 

D 

c 

64 

16 

J»  =  -0625  sec. 

c 

128 

26 

5V  =  '0384 

c' 

256 

47 

?V  =  -0212 

g' 

384 

60 

ifo  =  '0166 

c" 

512 

78 

TV  =  '0128 

e" 

640 

90 

Jb=  -0111 

g" 

768 

109 

Ti,  =  -0091 

c'" 

1024 

135 

^  =  -0074 

Column  N  gives  the  names  of  the  notes  corresponding  to  the  vibra- 
tions a  second  in  column  V.  The  c'  in  this  series  is  that  used  by  physi- 
cists generally,  and  gives  256  vibrations.  In  column  B  is  presented  the 
smallest  number  of  beats  a  second  which  the  corresponding  sound  must 
make  with  another  in  order  that  the  two  may  be  in  harmony,  or,  as  it 
is  generally  stated,  may  make  with  the  other  the  nearest  consonant  in- 
terval. If  47  beats  a  second  of  c',  for  example,  blend,  then  the  sensa- 
tion of  each  of  these  beats  remains  on  the  ear  ^  of  a  second.  In  column 
D  are  given  these  durations  in  fractions  of  a  second.  As  these  frac- 
tions are  the  lengths  of  time  that  the  sensation  lingers  in  the  ear  after 
the  vibrations  of  the  air  near  the  drum-skin  have  ceased,  they  are  very 
properly  called  the  durations  of  the  residual  sonorous  sensations. 

Observe,  in  the  table,  that  this  duration  becomes  shorter  as  the 
pitch  of  the  sound  rises.  Thus,  while  the  residual  sensation  of  C  is  ^ 
of  a  second,  that  of  c"'  is  only  ^. 

The  discord  produced  by  two  sounds,  Helmholtz  explains 
by  the  fact  that  the  sounds  produce  beats,  which  do  not 
blend  because  they  are  too  few  in  a  second;  but,  if  the 
two  sounds  be  gradually  made  to  differ  more  and  more  in 
pitch,  the  beats  increase  in  number  and  at  last  blend  into  a 
smooth,  continuous  sensation.  He  defines  discord  as  a  dis- 
continuous sensation,  harmony  as  a  continuous  sensation. 

The  beats  given  by  two  sounds  in  a  second  are  equal  to  the  differ- 
ence of  their  numbers  of  vibrations  in  a  second.  Thus,  if  we  had  one 
sound  given  by  256  vibrations  a  second  and  the  other  by  320,  their 
difference  is  54.  Our  table  shows  that,  for  256  vibrations,  only  47  are 
required  to  blend  into  a  continuous  sensation,  so  these  two  sounds  are 
in  harmony.  This  is  well  known,  for  they  are  the  sounds  of  c  and  of 
E,  and  form  the  major  third.  . 


418  SOUND. 

Suppose  we  had  two  sounds  falling  at  the  same  time  on  the  ear, 
one  of  256  the  other  of  303  vibrations  a  second.  The  difference  of 
these  numbers  is  47.  Referring  to  the  table,  we  see  that  the  sound  of 
256  vibrations  remains  on  the  ear  ^V  of  a  second ;  therefore  these  sounds 
just  form  a  harmonious  combination — the  minor  third  of  the  treble. 

Assume  that  the  c  of  256  vibrations  and  the  d  of  238  vibrations  a 
second  are  heard  simultaneously ;  the  difference  here  is  22,  but  47 
vibrations  are  required  to  produce  a  continuous  sensation.  Hence 
these  two  sounds  form  a  discord.  They  are  separated  only  by  a  tone 
on  the  piano.  Thus,  through  the  whole  musical  scale  we  can,  from  the 
table  given,  determine  beforehand  what  notes,  when  sounded  together, 
will  make  harmony,  and  what  notes  will  give  discord. 

QUESTIONS.— Describe  Faber's  talking-machine  ;  Edison's  Phonograph,  illustrat- 
ing the  principle  by  diagram.  What  use  has  been  made  of  the  phonograph  ? 
On  what  analogy  did  Helmholtz  construct  his  theory  of  Harmony  and  Discord  ? 
Explain  discord.  Give  Helmholtz's  definition  of  harmony  and  discord.  How 
may  we  determine  what  notes,  when  sounded  together,  will  make  harmony  ? 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

What  analogies  have  you  discovered  between  Sound  and  Heat  and  Light  ? 

The  steth'oscope,  employed  by  physicians  in  making  physical  examinations,  con- 
sists of  two  tubes,  terminating  at  one  end  in  a  flange  which  is  applied  to  the 
chest,  and  with  ivory  tips  at  the  opposite  extremities  of  the  tubes  for  insertion 
in  the  ears.  Explain  the  principle  by  which  healthy  and  abnormal  sounds  in 
the  heart  and  lungs  are  made  known  in  an  exaggerated  form  to  the  examiner. 

If  the  temperature  of  the  air  is  62°,  what  is  the  wave-length  of  a  sound  whose 
vibrations  are  280  to  the  second  ? 

What  is  the  cause  of  the  difference  between  a  bass  and  a  soprano  voice  ? 

What  kind  of  a  medium  is  required  for  the  transmission  of  sound-waves  ?  An 
elastic  medium,  which  may  be  solid,  liquid,  or  gaseous. 

If  a  sound  travels  a  half-mile  in  2£  seconds,  what  is  the  temperature  of  the  air  ? 

There  is  a  well  in  Carisbrooke  Castle,  Isle  of  Wight,  240  feet  deep.  How  much 
time  elapses  after  a  pebble  is  dropped  into  the  well  before  the  sound  of  the 
splash  reaches  the  ear  ? 

Does  confusion  arise  from  our  hearing  sounds  with  two  ears  ?  It  is  believed  that 
two  ears  possibly  correct  the  errors  of  each  other ;  they  certainly  help  us  to 
determine  the  place  whence  sounds  proceed. 

Why  was  it  possible  for  boys,  in  the  absence  of  actresses,  to  personate  success- 
fully on  the  Elizabethan  stage  the  heroines  of  Shakespeare^  plays  ? 

If  I  fire  a  gun  among  the  mountains  and  hear  the  first  echo  in  two  seconds,  about 
how  far  away  is  the  nearest  reflecting  surface  ? 

Why  do  shells  of  a  certain  shape  murmur  when  held  to  the  ear  ?  Because  they 
form  resonators  which  re-enforce  sounds  in  the  air.  How  ? 

How  many  miles  away  is  the  lightning  when  thunder  is  heard  22  seconds  after 
the  flash,  the  temperature  of  the  air  being  70°  Fahr.  ? 

Why  are  musical  instruments  provided  with  sounding-boards  ?  So  as  to  increase 
the  area  of  the  vibrating  surface,  and  thus  gain  in  intensity.  If  the  intensity  be 
increased  in  this  way,  remember  that  the  duration  of  the  sound  is  diminished 


MAGNETISM. 

NATURAL  AND  ARTIFICIAL  MAGNETS. 
Lodestones. — It  was  known  to  the  ancients  that  a  cer- 
tain black  mineral  possessed  the  power  of  attracting  small 
pieces  of  iron  or  steel.  This  mineral  was  an  ore  of  iron, 
called  by  the  Greeks  magnes,  from  Magnesia,  the  name  of  a 
city  iii  Asia  Minor,  near  which  it  was  procured.  Speci- 
mens of  the  same  magnetic  iron  are  now  found  in  various 
parts  of  the  earth  and  are  known  as  natural  magnets,  some- 
times lodestones  (leading -stones),  because  when  freely  sus- 
pended they  tend  to  point  north  and  south. 

The  pupil  may  prove  this  fact  by  hanging  a  piece  of  lodestone  in 
a  stirrup  of  copper  wire.  After  oscillating  for  a  few  seconds,  it  will 
come  to  rest  with  its  length  in  a  northerly  and  southerly  direction. 

Artificial  Magnets. — If  a  bar  or  other  piece  of  steel  be 
rubbed  with  a  natural  magnet,  it  will  acquire  the  properties 

NOTE.— With  the  apparatus  shown  above,  the  fundamental  principles  of  mag- 
netism may  be  illustrated.  Nos.  1  and  7  are  horseshoe-magnets ;  No.  2  shows 
bar-magnets ;  No.  3,  a  piece  of  steel  watch-spring ;  No.  4  is  a  magnetic  needle 
mounted  on  stand  ;  No.  5  is  a  sifter  for  iron-filings  (made  cheaply  by  removing 
the  bottom  from  a  tin  box  and  soldering  on  a  piece  of  fine  wire  gauze  in  its 
place) ;  No.  6  is  a  pocket  compass  ;  and  No.  8,  a  piece  of  lodestone.  This  outfit 
may  be  obtained  of  any  dealer  in  electrical  apparatus. 


420 


MAGNETISM. 


of  the  latter  and  become  itself  a  magnet,  attracting  iron- 
filings,  needles,  etc.  The  power  of  communicating  magnet- 
ism from  one  body  to  another  may  be  applied  indefinitely ; 
the  same  magnet  may  be  used  for  this  purpose  many  times 
without  losing  its  strength. 

A  piece  of  steel  to  which  magnetic  properties  have  been 
imparted  is  called  an  Artificial  Magnet. 

Natural  magnets  are  now  seldom  used  except  as  curiosities,  be- 
cause artificial  magnets  are  cheaper,  and  it  is  much  easier  to  make 
them  of  convenient  forms  than  is  possible  in  the  case  of  a  brittle  min- 
eral like  lodestone. 

Varieties  of  Artificial  Magnets. — There  are  several 
kinds  of  artificial  magnets,  called  from  their  shape  Bar- 
Magnets,  Horseshoe-Magnets,  and  Magnetic  Needles  (see  fig- 
ure, page  419).  It  is  possible,  however,  to  magnetize  a  piece 
of  steel  of  any  other  shape,  and  for  special  purposes  magnets 
have  been  made  in  the  form  of  spheres,  disks,  and  rings. 

A  magnet  is  usually  furnished  with  a  piece  of  soft  iron 
of  proper  size  and  form  to  develop  and  preserve  its  full  at- 
tractive power,  and  this  is  called  the  Arma- 
ture, or  keeper. 

Magnetic  needles  are  light  magnetic  bars,  gen- 
erally lozenge-shaped,  delicately  pivoted,  as  in  the 
pocket  compass,  or  suspended  by  a  strand  of  silk. 
The  needle  is  sometimes  placed  horizontally  on  a 
floating  cork  for  purposes  of  experiment. 

Compound  Mag-nets. — Let  the  pupil 
tie  a  number  of  knitting-needles  in  a  bun- 
dle and  then  rub  them  thoroughly  with  a 
FIG.  SOO.-COMPOUND  magnet  in  one  direction.  On  testing  the 
HORSESHOE-MAG-  needles  separately,  it  will  be  found  that 
only  those  which  were  on  the  outside  of 
the  bundle  have  become  strongly  magnet- 
ized. This  is  because  the  magnetic  effect  does  not  pene- 
trate very  far  from  the  outer  surface. 

The  same  fact  is  true  of  a  solid  bar  of  steel.     In  order, 


NET,  WITH  ARMA- 
TURE IN  PLACE. 


MAGNETIC  ATTRACTION.  421 

therefore,  to  make  a  large  powerful  magnet,  a  number  of 
steel  bars  are  magnetized  separately  and  then  riveted  to- 
gether. A  magnet  made  in  this  way  is  called  a  Compound 
Magnet,  and  may  have  either  the  bar  or  horseshoe  form. 


PROPERTIES  OF  MAGNETS. 

Attraction. — If  a  small  iron  nail  be  brought  in  contact 
with  a  natural  or  artificial  magnet,  it  will  be  attracted  by 
the  latter  and  may  be  lifted  from  the  table.  This  power  of 
attracting  iron  is  the  most  important  and  characteristic 
property  of  the  magnet,  and  almost  all  the  useful  applica- 
tions, as  well  as  the  scientific  experiments  of  magnetism, 
are  based  upon  it. 

Iron  is  not  the  only-  metal  attracted  by  the  magnet  \  cobalt  and 
nickel  are  similarly  influenced.  The  pupil  may  experiment  with  a 
bar-magnet  on  different  substances — paper,  leaves,  sawdust,  steel-fil- 
ings, pieces  of  lead,  copper,  and  zinc — and  thus  ascertain  for  himself 
what  bodies  are  magnetic. 

Magnets  not  only  attract  magnetic  substances,  but  are 
also  attracted  by  them  in  turn.  A  bar-magnet  suspended 
by  a  thread  is  drawn  toward  a  stationary  piece  of  iron. 

Although  the  attractive  power  of  lodestone  was  known  in  antiquity, 
it  was  regarded  merely  as  an  interesting  phenomenon  and  never  util- 
ized. Pliny  informs  us  that  Ptolemy  Philadelphus  proposed  to  build 
a  temple  at  Alexandria,  the  ceiling  of  which  was  to  be  of  lodestone, 
that  its  attraction  might  hold  an  iron  statue  of  his  queen  Ar-sin'-o-e 
suspended  in  the  air.  Death  prevented  Ptolemy  from  carrying  out  his 
design  ;  but  St.  Augustine,  at  a  later  day,  mentions  a  statue  thus  actu- 
ally held  in  suspension  in  the  temple  of  Se-ra'-pis  at  Alexandria. 

Attraction  through  Bodies. — A  magnet  attracts  a 
nail  through  a  board,  book,  or  plate  of  glass,  just  as  if  noth- 
ing intervened.  Through  an  iron  plate,  however,  the  at- 
traction is  reduced  or  entirely  checked. 

Magnetic  attraction  is  thus  transmitted  through  glass, 
wood,  or  other  non-magnetic  bodies,  very  nearly  as  well  as 


422 


MAGNETISM. 


ill 


FIG 


through,  air.  The  iron  plate,  however,  takes  up  the  magnetic 
effect,  being  itself  attracted,  and  so  prevents  the  force  from 
passing  through  and  reaching  the  nail. 

Attraction  takes  place  in  a  Vacuum ;  air  is 

not  essential  to  the  action  of  a  magnet. 

Polarity. — A  nail  is  attracted  much  more  forci- 
bly by  the  ends  of  a  magnet  than  by  the  middle  por- 
tion. A  bar-magnet  dipped  in  iron-filings 
becomes  thickly  coated  at  its  extremities ;  few 
filings  adhere  to  the  middle  of  the  bar.  This 
shows  that  the  greater  part  of  the  magnetic 
effect  is  concentrated  at  the  two  ends,  and 
they  are  called  the  poles  of  the  magnet. 

The  exact  parts  of  the 
poles  where  the  effects  are 
the  strongest  are  not  at 
the  extreme  ends  of  the 
magnet,  but  a  little  dis- 
tance inward.  From  these 
poles  the  attractive  power  decreases  almost  uniformly  toward  the 
center,  where  it  is  reduced  to  nothing.  The  line  of  disappearance  is 
called  the  neutral  line  of  the  mag- 
net. 

The  attractive  power  of  dif- 
ferent parts  of  a  bar-magnet  may      FlG  ^..MAGNET  DIPPED  IN  FILINGS. 
further  be  tested  by  means  of  the 

magnetic  pendulum,  an  iron  ball  suspended  by  a  thread  from  some 
convenient  point. 

North  and  South  Poles. — One  particular  pole  of  the 
needle,  if  suspended  by  a  string,  or  pivoted  as  in  the  ordinary 
pocket  compass,  will  always  be  found  to  turn  toward  the 
north.  This  is  therefore  called  the  north-seeking,  or  north 
pole ;  the  other,  the  south-seeking  or  south  pole. 

The  poles  of  a  magnet  are  usually  distinguished  by  the 
letters  N  and  S ;  but  sometimes  the  north  pole  has  merely  a 
line  filed  across  it,  and  is  called  the  marked  pole.  It  is  also 


.  301.— ATTRACTION  THROUGH 
A  GLASS  PLATE. 


GENERAL  LAW  OF  MAGNETISM. 


423 


distinguished  as  the  positive  (P)  or  +  pole,  in  which  case 
the  opposite  end  is  styled  the  negative  or  —  pole. 

Considerable  confusion  exists  in  re- 
gard to  the  names  of  the  magnetic  poles. 
In  this  country  and  in  England  the  poles 
are  generally  distinguished  as  stated 
above ;  but  the  French  call  the  pole 
which  points  north  a  south  pole,  while 
the  Chinese  attach  the  fleur-de-lis  to  the 
south  instead  of  the  north  pole.  The 
north  pole  is  sometimes  painted  red  and 
the  south  pole  blue. 


FIG.  303.— DIFFERENT  METHODS 
OF  MARKING  THE  POLES  OF 
MAGNETS. 


QUESTIONS.— State  what  you  know  of  the  history  of  Magnetism.  What  is  the 
origin  of  the  word  ?  What  is  lodestone  ?  Describe  its  properties.  Into  what 
two  classes  are  magnets  divided  ?  Why  are  artificial  magnets  preferable  to 
natural  stones  ?  How  are  artificial  magnets  made  ?  Name  several  varieties  of 
artificial  magnets.  What  is  an  armature  ?  Explain  the  principle  of  the  com- 
pound magnet. 

Mention  the  chief  properties  of  magnetism.  Describe  the  phenomena  of  attrac- 
tion. Is  iron  the  only  substance  attracted  by  a  magnet  ?  What  use  was  made 
of  magnetism  in  antiquity  ?  What  effect  on  attraction  has  a  board  or  piece  of 
glass  interposed  between  the  magnet  and  the  magnetic  body  ?  Does  attraction 
take  place  in  a  vacuum  ?  How  can  you  prove  your  answer  ?  What  would  be 
the  probable  effect  on  a  watch  if  a  bar-magnet  were  brought  near  it  ?  The 
balance-wheel  would  be  attracted,  and  the  watch  would  stop.  (Watches  are 
now  manufactured  whose  entire  escapement  is  made  of  metals  which  are  by 
nature  insensible  to  magnetism.) 

Explain  polarity.  Account  for  the  appearance  of  a  magnet  dipped  in  iron-filings. 
Where  does  the  greatest  attractive  force  reside  in  a  magnet  ?  Where  the  least  ? 
In  what  different  ways  are  the  north  and  south  poles  of  a  magnet  distinguished  ? 
Can  you  think  of  other  amusing  experiments  with  the  magnet  ?  (Suggestions  : 
Floating  objects  may  be  cut  out  of  cork  and  pieces  of  steel  imbedded  in  them. 
A  well  magnetized  steel  bar  concealed  in  a  piece  of  a  bamboo  cane  will  serve 
as  a  magic  magnetic  wand,  with  which  floating  figures  may  be  attracted  and 
repelled,  etc.)  Can  you  contrive  a  way  of  causing  a  threaded  needle  to  appear 
suspended  in  the  air  ? 


LAWS  AND  PRINCIPLES  OF  MAGNETISM. 

Law  of  Attraction  and  Repulsion. — If  a  compass 
and  a  magnet  be  brought  close  together,  the  two  north  poles 
and  the  two  south  poles  will  repel  each  other ;  but  the  south- 
seeking  pole  of  the  magnet  will  attract  the  north-seeking 


424 


MAGNETISM. 


pole  of  the  compass-needle,  and  vice  versa.  This  fact  gives 
rise  to  the  general  law :  Like  poles  repel  each  other,  unlike 
poles  attract  each  other. 

Balance  a  bar-magnet  with  weights  on  a  pair  of  scales.  Beneath 
its  positive  pole  bring  the  positive  pole  of  another  magnet,  and  the 
scale  containing  the 
bar  will  rise,  owing  to 
the  repulsion  of  the 
like  poles.  Substitute 
the  negative  pole,  and 
the  scale  will  descend, 
owing  to  the  attraction 
of  the  unlike  poles. 

The  mutual  repul- 
sion of  similarly  mag- 
netized bodies  is  inter- 
estingly illustrated  by 
Prof.  Mayer's  floating 
magnets.  A  number 

of  magnetized  sewing-needles  are  fixed  in  small  corks, 
so  that  they  will  float  in  a  basin  of  water  with  their 
points  down.  The  needles  arrange  themselves  in  sym- 
metrical groups,  according  to  their  number,  Fig.  305. 
If  a  bar-magnet  be  presented,  one  pole  will  be  found 
to  attract  the  floating  needles,  the  other  to  disperse 
them.  (Study  Fig.  304.) 

The  opposite  action  of  different  poles  may  be  further  illustrated  by 
suspending  a  steel  key  from  the  north  pole  of  a  bar-magnet,  and  mov- 
ing along  the  latter  a  second  magnet  of  the  same  size,  with  the  con- 


FIG.  304.— REPULSION  OF  MAGNE- 
TIZED SEWING-NEEDLES. 


FIG.  305. 


FIG.  306.— NEUTRALIZING  AC- 
TION OF  OPPOSITE  POLES. 


trary  pole  presented.     The  key  remains  suspended  until  the  two  poles 
are  sufficiently  near  to  neutralize  each  other's  action,  when  it  falls. 

The  Astatic  Needle. — The  tendency  of  two  exactly 
equal  magnetic  needles  to  point  north  may  be  neutralized 


INSEPARABILITY  OF  POLES.  425 

by  supporting  them,  with  their  poles  in  opposite  directions, 
on  the  same  pivot,  in  the  same  vertical  plane.  An  instru- 
ment thus  constructed  is  called  an  Astatic  Needle  (not 
standing  in  a  north  and  south  line) ;  it  does  not  seek  the 
north  pole,  but  remains  in  the  position  in  which  it  is  placed. 

The  Second  Law  of  magnetism  is  as  follows :  The 
force  exerted  between  two  magnetic  poles,  whether  attrac- 
tion or  repulsion,  is  directly  proportional  to  the  product  of 
their  strengths,  and  inversely  proportional  to  the  square 
of  the  distance  between  them. 

The  experimental  proof  of  this  law  is  measurably  difficult,  because 
it  requires  instruments  for  accurately  measuring  the  amount  of  the 
force  and  the  distance ;  but  a  few  trials  will  convince  any  observer 
that  the  force  between  two  poles  two  inches  apart  is  only  about  one 
quarter  as  great  as  at  a  distance  of  one  inch. 

The  Two  Poles  Inseparable. — A  piece  of  watch- 
spring,  even  though  magnetized  by  rubbing  it  with  only 
one  pole  of  a  magnet,  always  acquires 

two  poles,  one  north  and  one  south,    p § 

If  the  magnetized  watch-spring  be 

broken  into  a  number  of  pieces,  each    IN        S#N"       SJJN  _^s] 

piece  Will  be  found  to  have  two  poles,     FlG-  SW.-POLARITY  IN  PIECES 
,.,..,,  ,  ,,  OF  A  MAGNET. 

and  this  is  the  case  however  small 

the  pieces  may  be.  Both  parts  of  this  experiment  demon- 
strate the  principle  that  a  magnet  can  not  be  made  with  one 
pole  only.  Two  poles,  one  south  and  the  other  north,  must 
always  exist  together,  and  must  also  be  of  equal  total 
strength,  though  this  strength  may  be  differently  distributed. 

The  absolute  inseparability  of  the  two  poles  is  one  of  the  most  in- 
herent and  unchangeable  facts  in  magnetism.  It  is  explained  on  the 
principle  that  the  power  of  a  magnet  resides  in  its  molecules,  whose 
north  poles  are  all  turned  in  one  direction  and  the  south  poles  in 
another,  so  that  the  poles  of  magnetic  elements  intermediate  between 
the  extremities  of  the  magnet  neutralize  one  another.  The  magnetic 
force  is  thus  free  only  at  the  +  and  —  ends  of  the  magnet. 

If  the  broken  pieces  of  watch-spring  be  joined  again  so  as  to  form 
28 


426 


MAGNETISM. 


FIG.  308.— MAGNETIC  INDUCTION. 


a  single  magnet,  it  will  be  found  that  only  the  original  poles  exist,  the 
intermediate  poles  having  disappeared. 

Magnetic  Induction. — A  piece  of  soft  iron,  like  a  nail, 
when  brought  close  to  a  strong  magnet,  even  if  not  in  con, 
tact  with  it,  becomes  it- 
self a  magnet  and  will 
attract  a  tack  (see  Fig. 
308).  This  magnetizing 
action  of  a  magnet  on  other  bodies  is  called  Induction.  The 
polarity  induced  is  such  that  an  unlike  pole  is  created  in 
the  end  of  the  magnetic  substance  nearest  the  inducing  pole 
of  the  magnet,  and  a  like  pole  in  the  opposite  end,  as  shown 
in  the  figure. 

The  interposition  of  a  sheet  of  paper  or  glass,  the  hand, 
or  any  non-magnetic  substance,  between  N 
and  S,  will  not  interfere  with  the  inducing 
power  of  the  magnet. 

Induction  accounts  for  the  attraction  of  a  piece 
of  soft  iron.  An  unlike  pole  is  first  induced  in  the 
iron  and  then  attracted ;  and  this  effect  is  greater 
than  the  repulsion  of  the  like  pole  at  the  opposite 
end,  on  account  of  the  distance  of  the  latter.  Hence 
the  general  result  is  attraction. 

Soft  iron  armatures  become  magnets  by  induc- 
tion, and  then  by  induction  react  upon  their  mag- 
nets, thus  strengthening  the  power  of  the  magnets 
themselves.  The  rolling  armature,  shown  in  Fig. 
309  attached  to  a  U-shaped  magnet,  is  attracted  with 
such  force  that  when  the  magnet  is  held  in  a  verti- 
cal position  and  the  armature  descends,  instead  of 
falling  off  it  turns  the  poles  and  is  carried  by  its 
momentum  some  distance  up  the  opposite  side. 

The  Magnetic  Chain. — A  number  of  pieces  or  rings 
of  iron  may  be  suspended  from  a  magnet  in  the  form  of  a 
chain,  each  individual  in  the  series  becoming  by  induction 
a  temporary  magnet.  Carpet-tacks  may  be  used  in  making 
the  experiment.  If  the  tack  in  contact  with  the  magnet  be 


FIG.  309.  —  THE 
ROLLING  ARMA- 
TURE MAGNET. 


ARTIFICIAL  MAGNETS. 


taken  in  the  hand  and  the  magnet  withdrawn,  the  tacks  at 
once  lose  their  magnetism  and  fall  to  the  ground. 

It  will  be  found  that  a  given  magnet  will  support  a  certain  num- 
ber of  tacks  in  the  form  of  a  chain ;  but  when  a  second  magnet  is 
placed  beneath  the  chain,  so  that  its  south  pole  is 
under  the  north  pole  of  the  original  magnet,  the 
magnetic  power  in  the  poles  of  the  several  tacks 
will  be  increased  by  induction,  and  the  chain  may 
be  lengthened  by  the  addition  of  other  tacks. 

Let  the  pupil  explain  what  will  take  place  if 
the  lower  magnet  be  turned  round. 

Making    of   Artificial    Mag-nets. — 

There  are  various  methods  of  making  arti- 

ficial  magnets-  By  simPle  ru^bing  with  a 
piece  of  lodestone,  in  the  direction  of  the 
line  joining  its  poles,'  a  steel  bar  may  be  magnetized.  The 
method  by  single  touch  consists  in  rubbing  the  bar  with  the 
pole  of  a  permanent  magnet,  care  being  taken  that  the 
strokes  are  delivered  in  the  same  direction. 

In  magnetization  by  double  touch,  a  bar  of  hard  steel  is 
placed  horizontally,  and  the  op- 
posite poles  of  two  strong  mag- 
nets are  then  applied  to  the 
middle  of  the  bar  and  drawn 
apart  to  the  ends.  This  is  re- 
peated several  times ;  the  bar  is 
then  turned,  and  the  other  side 
treated  similarly.  It  will  now  be 
found  to  be  strongly  magnetized. 

Ketentivity. — A  hard  steel  bar,  magnetized  as  described 
in  the  last  experiment,  retains  a  large  part  of  the  magnet- 
ism. Soft  iron  treated  in  the  same  manner  retains  little  or 
no  magnetism.  Hence  we  say  that  hard  steel  has  great 
magnetic  retentivity,  or  coercive  force,  and  soft  iron  very 
little.  For  this  reason,  when  we  wish  a  magnet  to  retain 
its  power  permanently,  we  make  it  of  hard  steel. 


IlllliiiiiiiliiiiiiiW 


FIG.  311.— MAGNETIZATION  BY 
DOUBLE  TOUCH. 


428  MAGNETISM. 

Lifting  Power.  —  A  horseshoe-magnet  will  lift  a  load 
three  or  four  times  as  great  as  a  bar-magnet  of  the  same 
weight  (see  Fig.  312).  This  is  because  both  poles  of 
the  former  act  instead  of  one;  and,  furthermore, 
each  pole  increases  the  effect  of  the  other  by 
induction. 


This  lifting  power  is  the  simplest  test  of  the 
strength  of  a  magnet.  A  good  magnet  weighing  one 
pound  should  lift  twenty  pounds.  Small  magnets 
will  carry  relatively  more  weight  than  large  ones. 
Newton  is  related  to  have  worn  in  his  ring  a  piece 

of  lodestone  weighing  only  three  grains,  but  with  a 

"_,.,,         .          _-,       .        '     ,  FIG.  312.—  LIFTING 

carrying  power  of  746  grains.     Two  hundred  pounds      POWER  OF  BAR 

per  square  inch  of  surface  is  about  the  greatest  force      AND  HORSESHOE 
that  can  be  exerted.  MAGNET 

Preservation  of  Magnets.  —  Magnets  may  in  various 
ways  be  weakened  or  entirely  lose  their  power.  The  follow- 
ing precautions  should  therefore  be  observed  in  order  to 
keep  them  in  good  condition  : 

1.  Do  not  allow  a  horseshoe-magnet  to  remain  for  any  length  of 
time  without  its  armature.     Bar-magnets  are  generally  weak  because 
they  are  not  usually  provided  with  keepers.    Hence  they  should  be 
kept  either  in  pairs,  with  the  unlike  poles  together,  or  else  with  bars  of 
soft  iron  laid  alongside  to  act  as  keepers. 

2.  Do  not  put  two  magnets  away  with  their  like  poles  in  contact, 
because  each  will  tend  to  weaken  the  other  by  inducing  in  it  the  op- 
posite kind  of  magnetism. 

3.  Do  not  leave  a  magnet  with  its  south-seeking  pole  pointing 
north,  because  in  this  position  its  polarity  may  be  weakened  or  even 
reversed  by  the  magnetism  of  the  earth. 

4.  Do  not  allow  a  magnet  to  receive  rough  usage.    A  blow  or  fall 
will  disturb  the  magnetic  arrangement  of  the  molecules. 

5.  Do  not  heat  a  magnet,  as  heat  perceptibly  weakens  it.     The 
most  powerful  magnet  becomes  absolutely  demagnetized  at  a  red  heat, 
and  remains  so  after  cooling.     Magnetize  a  piece  of  knitting-needle, 
then  raise  it  to  a  red  heat,  and  you  will  find  that  it  has  entirely  lost 
its  magnetism. 

Lines  of  Force,  and  Magnetic  Field.  —  If  a  large 
card  or  glass  plate  be  laid  horizontally  on  a  bar-magnet  and 


LINES  OF  FORCE.  429 

fine  iron-filings  be  dusted  upon  it  with  a  sieve  or  "  colander  " 
(see  No.  5,  page  419),  the  filings  become  arranged  by  in- 


FIG.  313.— LINES  OP  FORCE  IN  CASE  OF  BAR-MAGNET. 

duction  in  peculiar  curves,  the  formation  of  which  is  aided 
by  gently  tapping  the  card  or  glass. 

These  curves  may  be  made  permanent  by  coating  the  glass  with 
paraffine  or  varnish  and  allowing  it  to  harden  before  the  filings  are 
sifted  upon  it.  After  the  curves  are  formed,  the  paraffine  or  varnish  is 
softened  by  heating  the  plate  over  a  spirit-lamp,  or  warming  it  in  an 
oven,  and  the  filings  sinking  into  the  film,  the  curves  become  fixed 
when  the  plate  cools.  Plates  thus  made  may  be  used  as  lantern-slides. 

The  curves  described  above  indicate  the  direction  and 
intensity  of  the  magnetic  force,  and  from  them  we  derive 
the  idea  of  lines  of  force.  It  should  be  remembered,  how- 
ever, that  lines  of  force  do  not  really  exist,  as  the  actu- 
al forces  them- 
selves are  not 
distributed  in 
lines,  but  fill 

the   entire  Space     FlG*  314-~ LlNES  OF  FORCE  BETWEEN  UNLIKE  AND  LIKE 

POLES. 

around  the  mag- 
net, which  space  is  called  the  Magnetic  Field. 

The  difference  between  the  curves  produced  by  unlike 
and  like  poles  is  shown  in  Fig.  314.  An  inspection  of  the 
lines  of  force  greatly  assists  the  mind  in  conceiving  how 


430  MAGNETISM. 

attraction  takes  place  in  the  first  case,  and  repulsion  in  the 
second.  Each  particle  of  iron  is  made  a  magnet  by  induc- 
tion and  places  its  longest  diameter  in  the  line  of  force  that 
passes  through  it ;  and  along  each  line  of  force  a  magnetic 
chain  is  formed  in  accordance  with  principles  already  ex- 
plained. 

Nearly  fill  one  of  your  test-tubes  with  iron-filings  and  then  stroke 
it  several  times  with  a  powerful  magnet.  The  particles  of  iron  will  be 
seen  to  set  themselves  in  the  direction  of  their  lengths. 

QUESTIONS.— State  the  law  of  Attraction  and  Repulsion.  By  what  experiments 
can  you  illustrate  it  ?  Give  the  details  of  Prof.  Mayer's  experiments  with  float- 
ing magnets.  If  you  lay  a  bar-magnet  on  a  table  with  its  N  pole  projecting 
over  the  edge,  and  allow  an  iron  nail  to  cling  to  its  under  side,  state  and  explain 
what  will  occur  when  the  S  pole  of  a  second  magnet  is  brought  over  and  near 
the  N  pole  of  the  first.  Describe  the  astatic  needle. 

What  is  the  second  law  of  magnetism  ?  Its  experimental  proof  ?  Account  for 
the  fact  that  each  piece  of  a  magnet  has  its  own  poles.  Explain  Magnetic  In- 
duction. How  does  it  account  for  the  attraction  of  iron  ?  How,  for  the  strength- 
ening effect  of  the  armature  ?  "Why  is  less  force  required  to  pull  a  small  iron 
rod  away  from  the  poles  of  a  powerful  horseshoe-magnet  than  to  detach  a  thick 
piece  of  iron  ?  Describe  the  rolling  armature  ;  the  magnetic  chain  ;  different 
methods  of  making  artificial  magnets.  How  would  you  magnetize  a  sewing- 
needle  so  that  the  point  shall  be  a  north-seeking  pole  ? 

What  is  Retentivity  ?  Suppose  that  two  rods  are  handed  you,  one  of  iron  and 
the  other  of  steel ;  also,  a  compass-needle  and  a  bar-magnet.  Describe  experi- 
ments whereby  you  can  ascertain  which  is  the  iron  rod.  Compare  the  lifting 
power  of  horseshoe  and  bar  magnets.  What  methods  are  suggested  for  pre- 
serving the  strength  of  magnets  ?  Give  reasons  in  each  case.  What  are  lines 
of  force  ?  Describe  the  magnetic  field.  If  two  long  iron  wires  are  suspended 
from  the  same  pole  of  a  magnet,  will  they  hang  parallel  ?  Why  ? 


THE  EARTH'S  MAGNETISM. 

The  Earth  a  Great  Magnet. — The  direction  assumed 
by  a  magnetized  needle  is  called  the  Magnetic  Meridian. 
The  fact  that  the  needle  places  itself  in  the  magnetic  me- 
ridian shows  that  the  earth  acts  as  if  it  contained  a  great 
magnet,  some  of  whose  lines  of  force  pass  along  the  ground, 
while  others  lie  entirely  within  the  earth  itself. 

The  action  of  the  earth  on  the  compass-needle  is  exactly 
the  same  as  that  of  a  permanent  magnet.  A  steel  bar  is 


DECLINATION  AND  DIP.  431 

temporarily  magnetized  by  induction  when  pointed  toward 
the  magnetic  pole  of  the  earth,  as  it  is  when  brought  near 
the  pole  of  a  magnet;  if  struck  a  blow  in  the  direction  of 
its  length  when  so  pointed,  it  remains  permanently  magnet- 
ized. (Let  the  pupil  make  these  experiments.) 

Magnetic  Pole  of  the  Earth. — The  magnetic  needle 
does  not  generally  point  exactly  toward  the  true  north.  If 
we  carefully  compare  the  direction  in  which  the  compass- 
needle  points  with  the  true  north  line,  determined  by  the 
north  star,  we  shall  find  that  the  two  do  not  in  most  locali- 
ties correspond. 

This  shows  that  the  magnetic  pole  of  the  earth,  toward 
which  the  needle  points,  is  not  situated  at  the  same  place  as 
the  geographical  pole.  A  negative 
magnetic  pole,  however,  must  be  in 
the  neighborhood  of  the  geographi- 
cal north  pole  in  order  to  attract 
the  +  P°le  of  the  needle. 

The  angle  between  a  true  north 
and   south  line   and  the   direction 
of  the  needle  is  called  the  Declina- 
tion of  the  Compass.     It  amounts 
to  twenty  degrees,  or  even  more  in       FlG  315._DECLINATION. 
some  localities ;  while,  in  the  ab- 
sence of  local  disturbance,  there  is  no  declination  at  places 
on  a  line  with  the  true  and  the  magnetic  pole. 

Declination  is  subject  to  variations  extending  through  long  peri- 
ods of  years.  At  London,  where  magnetic  observations  have  been 
made  since  1580,  the  declination  was  in  that  year  IV  17'  E. ;  in  1657, 
it  had  become  reduced  to  nothing,  and  the  compass-needle  pointed  to 
the  true  north.  In  1816,  it  reached  its  greatest  value  of  24°  30'  W. 
In  1888,  it  was  only  17°  40'  W. 

Magnetic  Dip.— If  a  needle  be  balanced  so  as  to  be 
horizontal  when  suspended  by  a  thread,  and  then  be  mag- 
netized, it  will  not  only  place  itself  in  the  vertical  plane  of 
the  magnetic  meridian,  but  will  point  downward  at  places 


432  MAGNETISM. 

in  the  northern  hemisphere.  The  angle  at  which  it  is  in- 
clined to  the  horizon  is  called  the  Dip  or  Inclination  of  the 
needle,  and  is  due  to  the  fact  that  the  earth  is  round,  and 
the  magnetic  pole  is  there- 
fore not  on  a  horizontal  line 
with  the  compass,  but  be-  ^_^_^ 

low  such  a  line. 

This  is  illustrated  in  Fig.  316, 
in  which  the  line  A  B  represents 
the  true  axis  of  the  earth,  P  the 
magnetic  pole,  N  S  a  dipping- 
needle,  pointing  at  the  pole,  and 
C  D  a  horizontal  line  through  the 
center  of  the  needle.  The  angle 

between  the  needle  and   the  line 

«  TV  .    , ,       -, .  FIG.  316.— DIP  OR  IN- 

C  D  is  the  dip.  CONATION. 

A  sphere  of  lodestone  causes  a 
small  needle  carried  over  its  surface  to  dip,  thus  illustrating  the  action 
of  the  earth. 

Useful  Applications  of  Magnetism.  —  Permanent 
magnetism  has  few  practical  applications.  Magnetism 
when  produced  by  electric  currents  (see  page  506),  is  much 
more  powerful  and  more  conveniently  applied. 

Almost  the  only  use  made  of  the  permanent  magnet  is 
in  the  Mariner's  Compass.  This  consists  of  one  or  more 
magnetic  needles  attached  to  the  lower  face  of  a  circular 
card,  delicately  pivoted,  and  generally  immersed  in  a  liquid 
so  as  to  decrease  the  pressure  upon  the  pivot.  The  circum- 
ference of  the  card  is  divided  into  degrees,  and  also  into 
thirty-two  "  points  of  the  compass."  It  is  supported  in 
such  a  manner  that  the  card  may  always  be  horizontal,  not- 
withstanding the  motion  of  the  vessel.  The  needles  re- 
main in  the  magnetic  meridian,  with  which  a  ship's  course 
may  readily  be  compared. 

The  Mariner's  Compass  was,  according  to  some  authorities,  in- 
vented in  China,  and  made  known  to  Europeans  through  the  instru- 
mentality of  the  Mohammedan  Arabs.  The  first  mention  of  the  use 


APPLICATIONS  OF  MAGNETISM. 


433 


of  the  magnetic  needle  in  Christian  Europe  occurs  in  a  curious  Pro- 
vengal  poem,  written  in  1190.  Early  accounts  of  the  instrument  de- 
scribe it  as  a  simple  iron  needle  magnetized  and  placed  on  a  pivot,  or 
floated  on  a  cork  in  a  vessel  of 
water,  in  either  case  free  to 
turn  in  any  direction. 

The  magnetism  induced  in 
iron  ships  by  the  action  of  the 
earth's  force,  in  connection  with 
the  constant  hammering  during 
the  process  of  building,  causes 
a  serious  deviation  of  the  com- 
pass, for  which  allowance  has  to 
be  made  in  determining  the  true 
direction. 


FIG.  317.— COMPASS-CARD. 


Permanent  magnets 
have  been  used  for  separat- 
ing magnetic  iron-ore  from 
the  sand  with  which  it  occurs.  The  surgeon  sometimes  has 
recourse  to  the  magnet  to  remove  from  the  eye  particles  of 
steel  or  iron  so  situated  as  to  render  their  extraction  with 
ordinary  instruments  difficult,  if  not  impossible.  To  deter- 
mine the  presence  of  steel  in  any  of  the  tissues,  a  powerful 
magnet  is  held  for  fifteen  minutes  on  the  injured  part,  thus 
magnetizing  the  impacted  fragments.  Their  exact  location 
may  then  be  ascertained  by  the  dip  of  a  delicately  sus- 
pended needle.  Sewing-needles,  accidentally  forced  into 
the  flesh,  have  been  brought  within  reach  by  the  persistent 
action  of  strong  magnets. 


QUESTIONS.— What  is  the  Magnetic  Meridian  ?  The  behavior  of  the  compass- 
needle  proves  what  in  regard  to  the  earth  ?  If  you  were  required  to  make  a 
model  illustrating  the  magnetic  properties  of  the  earth  by  putting  a  bar-mag- 
net inside  a  ball  of  clay,  show  by  a  sketch  how  you  would  place  the  magnet, 
and  explain  how  the  magnetic  properties  of  the  model  would  correspond  with 
those  of  the  earth.  Explain  Declination  ;  Dip.  To  what  variations  is  declina- 
tion subject  ? 

Describe  the  Mariner's  Compass.  Relate  what  is  known  of  its  history.  How  is  it 
affected  by  the  plates  of  iron  ships  ?  How  are  such  plates  magnetized  ?  What 
then  has  to  be  made  in  determining  true  direction  ?  For  what  purpose  has  the 
magnet  been  utilized  by  the  mineralogist  ?  By  the  surgeon  ? 


434  MAGNETISM. 


MISCELLANEOUS   QUESTIONS  AND  PROBLEMS. 

Why  does  not  the  needle  in  your  pocket-compass  dip  ? 

State  what  you  think  would  be  the  effect  of  adding  daily  a  little  to  the  weight 
which  a  magnet  supports.  Of  overloading  a  magnet. 

Why  does  not  a  freely  floating  needle  move  bodily  toward  the  north  magnetic 
pole  ?  Because  the  forces  that  have  brought  it  into  the  magnetic  meridian  are 
then  equal,  opposite,  and  in  the  same  line. 

Why  is  a  compass  untrue  in  the  neighborhood  of  iron  or  steel  ? 

If  a  horseshoe-magnet  be  placed  near  a  compass-needle,  it  will  move  the  needle 
a  little  way  round  ;  but  if  a  piece  of  soft  iron  be  laid  across  the  poles  of  the 
magnet,  the  needle  will  move  back  toward  its  natural  position.  Explain  this. 

If  you  have  three  equal  bar-magnets  without  keepers,  how  would  you  arrange 
them  so  that  when  not  in  use  they  may  preserve  their  magnetism  ? 

Explain  magnetic  polarity,  and  the  law  of  magnetic  behavior. 

How  may  the  polarity  of  two  needles  of  equal  power  be  destroyed  ? 

What  are  the  magnetic  poles  of  the  earth  ? 

What  would  be  the  position  of  the  needle  at  the  north  magnetic  pole  ?  It  would 
stand  vertical,  with  its  north  pole  toward  the  earth.  Describe  its  position  at 
the  south  magnetic  pole. 

Illustrate  the  variations  to  which  Declination  is  subject. 

What  is  a  line  of  no  variation  ?  A  line  along  which  the  declination  does  not 
vary.  Columbus  discovered  such  a  line  east  of  the  Azores  (see  page  8,  Apple- 
tons1  Physical  Geography).  Aware  of  the  change  in  the  direction  of  the  needle, 
with  a  change  of  place,  it  seemed  to  him  as  if  he  were  indeed  "  entering  a  new 
world  "  in  which  the  very  laws  of  Nature  were  at  fault. 

Is  the  cause  of  the  earth's  magnetism  understood  ?    It  is  not. 

It  has  often  been  attempted  to  make  magnetic  "perpetual-motion  machines." 
The  usual  plan  has  been  to  attach  a  number  of  pieces  of  iron  to  the  rim  of  a 
wheel  revolving  near  the  poles  of  a  magnet,  and  to  place  between  the  magnet 
and  the  wheel  a  magnetic  screen,  covering  the  half  of  the  wheel  below  the 
magnet.  In  this  way,  the  pieces  of  iron  on  the  upper  side  of  the  wheel  would 
be  drawn  toward  the  magnet ;  but  it  was  supposed  they  would  pass  behind 
the  screen  upon  reaching  the  point  in  their  path  nearest  the  magnet,  and  would 
then  cease  to  be  attracted.  Hence  they  would  freely  move  away  from  the 
magnet  on  the  lower  side  of  the  wheel.  Thus  there  is  apparently  quite  a  strong 
tendency  for  the  wheel  to  keep  on  revolving  in  one  direction  perpetually,  or 
until  the  machine  wears  out.  There  is,  of  course,  a  fallacy  in  this,  as  in  all 
other  "perpetual-motion  machines1'  (turn  to  page  148).  What  is  it?  We 
have  learned  that  attraction  takes  place  through  all  non-magnetic  substances 
almost  equally  well ;  therefore,  there  is  no  known  screen  or  shield  for  mag- 
netism except  iron,  or  some  other  magnetic  material.  But  such  a  screen  takes 
up  the  lines  of  force  itself,  and  would  therefore  weaken  the  attraction  of  the 
magnet  for  the  upper  pieces  of  iron  on  the  wheel.  Even  if  a  perfect  magnetic 
shield  were  found,  a  machine  of  this  kind  would  not  work,  because  the  mag- 
netic lines  of  force  would  curve  around  behind  the  shield  (see  page  429)  and 
hold  the  lower  pieces  of  iron  back  exactly  as  much  as  the  upper  pieces  are 
drawn  forward,  and  hence  the  wheel  would  stand  still. 


ELECTRICITY. 

ELECTRICAL  PHENOMENA.— POTENTIAL. 

Electricity  and  Heat  compared. — When  we  are  sub- 
jected to  variations  of  temperature,  as  near  a  furnace  or  a 
load  of  ice,  we  experience  sensations  and  observe  phenom- 
ena which  we  attribute  to  an  agent  called  Heat. 

Neighboring  bodies  at  times  also  differ  from  one  another 
in  a  manner  which  produces  other  phenomena,  and  these 
we  refer  to  an  agent  known  as  Electricity.  The  phenomena 
of  electricity  were  first  observed  in  the  clouds  as  thunder 

NOTE.— In  the  illustration  above  are  shown  a  typical  electrical  machine  (3), 
condenser  (2),  and  discharger  (4),  with  a  gravity-cell  (1),  the  principle  of  action  in 
the  case  of  each  generator  of  electricity  being  explained  in  the  following  chap- 
ter. A  class  provided  with  these  articles  (furnished  by  all  prominent  dealers  in 
electrical  instruments),  and  such  other  simple  apparatus  as  can  easily  be  impro- 
vised in  accordance  with  directions  given  in  the  text,  will  be  enabled  to  perform 
the  fundamental  experiments  in  electricity.  It  is  recommended  that  there  be 
added  a  glass  rod  and  a  rod  of  shellac  or  vulcanite  for  excitation,  a  cat's  skin 
as  an  exciter,  a  dozen  pith-balls,  a  few  gold  leaves,  and  a  yard  or  two  of  copper 
wire.  Cheaper  electric  machines  may  be  purchased  or  constructed  by  the  in- 
genious pupil ;  but  the  Toepler-Holtz  (shown  above)  is  by  far  the  most  satisfac- 
tory, giving  brilliant  discharges  and  working  under  all  atmospheric  conditions. 


436  ELECTRICITY. 

and  lightning.  They  were  produced  artificially  by  rubbing 
amber  (in  Greek,  electron)^  perhaps  600  years  B.  c. ;  but 
Benjamin  Franklin  first  showed  that  the  electricity  of  am- 
ber was  identical  with  that  of  the  clouds. 

Differences  of  temperature  are  continually  obliterated  by  the 
transmission  of  heat  from  hot  bodies  to  neighboring  cooler  ones. 
Electrical  differences  are  more  quickly  equalized,  hence  their  phe- 
nomena are  less  frequently  noticed  in  Nature,  unless  instrumental 
methods  of  observation  are  used. 

The  savage  sees  little  of  heat  except  in  the  fluctuations  of  the 
weather  and  in  his  camp-fire.  In  civilized  life,  we  meet  it  in  furnace 
and  forge,  in  our  gas-flames,  in  the  bearings  of  machinery,  in  chemical 
reactions,  and  in  thousands  of  cases  where  it  is  used  in  the  arts. 

During  the  last  ten  years,  electrical  phenomena  have  become  more 
commonly  known  through  similar  applications  of  electricity. 

Potential. — When  neighboring  bodies  differ  in  such  a 
way  that  electrical  phenomena  are  observed  in  the  region 
between  them,  the  bodies  are  said  to  be  at  different  poten- 
tials. Two  clouds  which  differ  sufficiently  in  potential  will 
be  connected  by  a  flash  of  lightning.  If  a  stick  of  sealing- 
wax  or  a  cake  of  resin  be  rubbed  with  a  piece  of  flannel  or 
a  cat's  skin,  the  two  bodies  will  assume  different  potentials. 
They  are  said  to  be  electrified,  as  a  body  of  high  temperature 
is  said  to  be  heated. 


PROPERTIES  OF  ELECTRIFIED  BODIES. 

An  Electrified  Body  brought  near  to  any  other  un- 
charged body  of  different  potential  will  attract  it.  If  the 
second  body  is  easily  movable,  it  will  be  drawn  toward  the 
first.  Small  pieces  of  paper,  pith-balls,  a  soap-bubble,  a  toy 
balloon,  or  a  light  pendulum  of  any  material,  will,  under 
such  circumstances,  be  attracted ;  and  a  water-jet  from  a 
siphon  or  hydrant  will  be  deflected  into  a  curve  instead  of 
falling  in  a  vertical  line  (see  Fig.  319).  If  a  hard  rubber 
pen-holder  or  large  glass  tube  be  vigorously  rubbed  with  a 


ELECTRICAL  ATTRACTION  AND  REPULSION.      437 


silk  handkerchief,  it  will  serve  as  the  electrified  body  in  the 
experiments  just  described. 

In  a  dark  room,  flashes  of  light  may  be  seen  during  the  rubbing  of 
the  two  bodies,  accompanied  with  a 
crackling  sound ;  and  by  presenting 
the  knuckle  to  the  electrified  body, 
faint  sparks  are  sometimes  observed. 
A  peculiar  odor  is  perceived  when 
such  sparks  are  produced;  in  the 
case  of  lightning  which  strikes  the 
earth,  it  is  always  noticed  by  per- 
sons in  the  vicinity.  This  odor  is 
that  of  ozone,  a  colorless  gas  formed 
from  the  oxygen  of  the  air. 

The  face  when  brought  near 
the  excited  body  feels  as  if  a  cob- 
web were  in  contact  with  it — a  sen- 
sation really  due  to  air-currents 
which  are  repelled  from  the  body 
against  the  face.  FIG.  319.— DEFLECTION  OF  WATER-JET. 

Attractions  and  Repulsions. — If  a  pith-ball  hung  on 
a  silk  fiber  is  allowed  to  touch  the  attracting  body,  it  will, 
after  a  few  moments,  be  repelled,  as  shown  in  Fig.  320.     If 
the  ball  be  followed  up  by  the  electrified  body,  it  will  be 
continually  repelled  (see  page  53).     Grasp  the 
pith-ball  in  the  hand.     The  electricity  will  be 

conducted  away,  and 
it  will  then  be  at- 
tracted as  before  (Fig. 
321).  If  the  pith- 
ball  be  gilded,  it  will 
be  repelled  the  in- 
stant it  touches  the 
electrified  body. 

Hang  a  small  glass  tube  in  a  wire  stirrup,  the  ends  of  which  are 
tipped  with  globules  of  solder,  and  suspend  the  whole  on  a  silk  fiber, 
as  shown  in  Fig.  322.  Another  glass  tube  which  has  been  excited  by 
friction  with  silk  will  attract  either  end.  Allow  the  tubes  to  come  in 


FIG.  320.— REPULSION.       FIG.  321.— ATTRACTION. 


438 


ELECTRICITY. 


contact ;  repulsion  will  not  follow.  If,  however,  a  metal  rod  be  sub- 
stituted for  the  swinging  glass  tube,  either  end  will  be  attracted ;  but 
if  contact  is  allowed  to  take  place,  the 
metal  rod  will  finally  be  repelled.  The 
end  which  was  not  touched  will  also  be  re- 
pelled. 

Coat  a  glass  rod  with  an  alcoholic  solu- 
tion of  shellac,  ignite  the  shellac,  and 
while  the  tube  is  hot  cover  it  with  tin- 
foil. It  will  now  behave  like  the  metal 
rod. 


FIG.  322.— GLASS  TUBE  IN 
WIRE  STIRRUP. 


Conduction  of  Electricity. — Apparently  the  electric- 
ity is  communicated  from  the  attracting  to  the  suspended 
body.  If  the  suspended  body  is  metallic  or  has  a  metallic 
coating,  the  electricity  is  quickly  diffused  over  the  whole 
surface  ;  but,  in  order  to  electrify  the  glass  tube,  every  part 
of  it  must  be  brought  in  contact  with  the  electrified  body. 
The  metal  is  said  to  conduct  the  electricity. 

Bodies  that  transmit  electricity  freely,  like  metals,  living 
plants  and  animals,  and  water,  are  known  as  Conductors ; 
those  that  do  not,  as  silk,  glass,  feathers,  hard  rubber,  and 
air,  are  called  Non-conductors  or  Insulators. 

Electrify  a  stick  of  sealing-wax  by  rubbing  it  with  flannel,  and 
present  it  to  a  suspended  stick  of  sealing-wax  which  has  been  similarly 
treated.  The  sticks  will  repel  each  other.  Two  glass  rods  rubbed 
with  a  silk  handkerchief  will  also  repel  each  other ;  but  an  electrified 
glass  rod  and  an  electrified  stick  of 
sealing-wax  will  attract  each  other. 
Either  may  be  suspended  in  the  wire 
stirrup,  and  the  other  may  then  be 
presented  to  it. 

The  pith-ball,  when  unelectrified, 
will  be  attracted  either  by  the  glass 
rod  or  the  stick  of  sealing-wax.  Elec- 
trify it  by  allowing  it  to  come  in  con- 
tact with  either.  That  body  (for  ex- 
ample, the  glass  rod)  will  then  repel  it.  The  other  body  (in  this  case 
the  sealing-wax)  will  then  attract  it. 

Suspend  two  gilded  pith-balls  on  silk  fibers  from  a  common  sup- 


FIG.  323. 


CONDUCTION  OF  ELECTRICITY.  439 

port,  so  that  they  hang  in  contact  with  each  other.  Then  electrify 
them  by  contact  with  the  excited  glass  rod.  They  will  immediately 
fly  apart  (see  Fig.  323).  Bring  the  glass  rod  up  under  the  two  balls, 
and  they  will  be  repelled  more  widely.  If  the  excited  sealing-wax  be 
placed  in  the  same  position,  the  balls  will  then  be  drawn  together, 

Present  the  flannel  used  in  rubbing  the  sealing-wax,  and  the  balls 
will  diverge  more  widely.  The  flannel  behaves  like  the  glass  rod,  and 
repels  when  the  sealing-wax  attracts. 

In  a  similar  way  it  may  be  shown  that  when  any  two  un- 
like bodies  are  rubbed  together  they  both  become  electrified, 
and  that  when  one  will  attract  the  other  will  repel  a  third 
electrified  body. 

In  some  cases  it  is  necessary  to  insulate  the  bodies  on  supports  of 
glass  or  hard  rubber,  to  prevent  the  escape  of  the  electricity.  This  is 
the  case  with  flannel  and  silk,  which  become  slightly  moist  from  the 
hand ;  also  with  a  metal  tube,  which  must  be  provided  with  a  glass 
handle.  Why? 

When  the  two  bodies  which  have  been  rubbed  together  are  held 
in  contact,  they  act  equally  in  opposite  directions  on  any  third  body. 
The  resulting  force  is  zero. 

Positive  and  Negative  Electricity. — If  the  electric- 
ity of  the  two  bodies  is  added  together,  the  bodies  become 
^electrified.  These  charges  of  electricity  behave  like  equal 
positive  and  negative  quantities. 

On  this  account,  these  electricities  are  called  positive  and 
negative  electricities.  No  reason  is  known  for  calling  one 
of  them  positive  rather  than  the  other.  The  electricity  of 
glass  when  rubbed  with  silk  is  called  positive,  and  that  of 
resin  or  sealing-wax  negative.  A  body  charged  with  -f- 
electricity  is  said  to  have  a  +  potential,  while  a  body  nega- 
tively charged  has  a  —  potential. 

Any  two  bodies  which  differ  even  in  temperature,  will 
when  rubbed  together,  become  not  only  heated,  but  also 
electrified. 

Potential  Series. — In  the  following  list,  the  substances 
are  named  in  such  order  that  if  any  two  of  them  are  rubbed 


440  ELECTRICITY. 

together  the  one  first  named  in  the  series  becomes  positively 
electrified,  while  the  other  becomes  negatively  electrified  : 

1.  Cat's  skin.  5.  Glass.  9.  Wood.  13.  Resin. 

2.  Flannel.  3.  Cotton.  10.  Metals.  14.  Sulphur. 

3.  Ivory.  7.  Silk.  11.  Caoutchouc.  15.  Gutta-percha. 

4.  Rock  crystal.  8.  The  hand.  12.  Sealing-wax.  16.  Gun-cotton. 

Positive  and  negative  electricity  are  related  to  each  other  some- 
what as  heat  and  cold. 

In  a  room  where  all  objects  have  the  same  temperature,  two  bodies 
rubbed  together  become  heated,  in  most  cases  unequally.  The  phe- 
nomena of  heat  would  resemble  those  of  electricity  if  the  temperature 
of  one  of  the  bodies  was  raised  and  that  of  the  other  diminished.  To 
carry  out  the  analogy,  if  the  two  bodies  had  originally  the  temperature 
of  the  hand,  one  would  grow  cool  and  the  other  warm  by  friction.  If 
left  in  contact,  the  bodies  would  become  wwheated  again,  as  two  elec- 
trified bodies  become  wwelectrified  under  similar  conditions. 

The  following  Laws  of  Electric  Attraction  and 
Repulsion  have  been  determined  :  — 

1.  Electric  charges  of  like  signs  repel  each  other  ;  elec- 
tric charges  of  opposite  signs  attract  each  other. 

2.  The  force  with  which  each  of  two  charges  attracts  or 
repels  the  other,  is  directly  proportional  to  the  product  of 
the  two  quantities  of  electricity,  and  inversely  proportional 
to  the  square  of  the  distance  between  them. 

The  Unit  Quantity  of  Electricity  is  the  quantity 
which  will  attract  an  equal  quantity  of  opposite  sign  at  a 
distance  of  1  cm.,  with  a  force  of  one  dyne  (see  page  90). 

Suppose  a  unit  quantity  to  be  placed  on  a  small  sphere  at  A  (Fig. 
324),  and  an  equal  quantity  on  a  sphere  B,  the  distance  between  the 
centers  of  the  spheres  being  one  centimetre.  The  spheres  would  be 
pulled  together  with  a  force  of  one  dyne.  Two  spheres  at  B  would 
each  attract  A  with  the  same  force.  If  the  two  charges  at  B  were  on 


A  B  A  B  A  B 

FIG.  324.—  ILLUSTRATING  ATTRACTION  BETWEEN  UNIT  QUANTITIES  OF  ELECTRICITY. 

one  body,  the  combined  attraction  on  A  would  be  two  dynes.     A 
would  also  attract  each  of  the  two  with  a  force  of  one  dyne,  and  would 


THE  ELECTROSCOPE. 


441 


attract  two  units  at  B  with  a  force  of  two  dynes.  Two  units  at  A 
would  each  attract  the  two  units  at  B  with  a  force  twice  as  great  as 
that  exerted  by  one  unit.  The  attraction  of  two  units  at  A  upon  two 
units  at  B  would  therefore  be  four  dynes,  which  is  in  all  these  cases 
the  product  of  the  two  quantities.  Similarly,  m  units  at  A  would 
attract  m'  units  at  B  with  a  force  of  m  m'  dynes. 

By  doubling  the  distance,  the  force  becomes  one  fourth  as  great. 
At  three  times  the  distance,  it  is  one  ninth  as  great,  etc.  These  two 
laws  have  been  proved  by  experiment  with  very  great  precision. 


The  formula  which  represents  these  laws  is  / ; 


m  m' 


If  m  =  5,  m'  =  3,  and  d 


5x3 


•  20  cm.,  then  f  =  — -  =  0'0375  dyne. 


QUESTIONS.— What  is  the  derivation  of  the  term  Electricity  ?  Can  you  discern  any 
relation  between  electricity  and  heat?  When  were  the  phenomena  of  elec- 
tricity first  known  ?  How  are  differences  of  temperature  obliterated  ?  How, 
electrical  differences  ?  Explain  Potential.  When  the  potential  of  bodies  dif- 
fers, what  must  take  place  ?  Explain  the  most  noticeable  property  of  an 
electrified  body.  What  simple  experiments  can  you  suggest  to  illustrate  it  ? 
What  is  ozone,  and  how  is  it  produced  ?  Describe  and  explain  the  sensation 
when  the  face  is  brought  near  an  excited  body. 

State  the  law  of  electric  Attraction  and  Repulsion.  How  may  it  be  illustrated  with 
suspended  pith-balls  ?  With  swinging  glass  tubes  and  metal  rods  ?  Explain  what 
is  meant  by  a  Conductor  ;  by  a  Non-conductor  ;  by  positive  and  negative  elec- 
tricity. Suppose  rods  of  glass,  iron,  sealing-wax,  and  copper,  to  be  rubbed  with 
a  silk  handkerchief  ;  which  will  attract  pieces  of  paper  ?  The  pieces  of  paper 
attracted  by  the  electrified  rod  are  repelled  after  they  touch  it.  Why  ?  To 
what  extent  is  the  relation  between  positive  and  negative  electricity  analogous 
to  that  between  heat  and  cold  ?  Define  the  unit  quantity  of  electricity  ? 


METHODS  OF  ELECTRIFICATION. 

The  Electroscope. — The  attractions 
and  repulsions  of  electrified  bodies  are 
studied  by  means  of  the  electroscope. 

A  very  simple  form  of  this  instrument  is 
shown  in  Fig.  325.  It  consists  of  a  clean  flask 
provided  with  a  rubber  stopper,  through  which 
passes  a  tube  of  hard  rubber.  Within  this  tube 
is  a  rod  made  of  stiff  copper  wire.  Attached  to 
the  lower  end  of  the  rod  are  two  small  gold  leaves, 
which  hang  side  by  side.  Soldered  to  the  upper 
end  of  the  rod  is  a  brass  or  tin  plate  one  or  two 
29 


FIG.  325.— GOLD-LEAF 
ELECTROSCOPE. 


442 


ELECTRICITY. 


inches  in  diameter.     A  hole  should  be  bored  through  this  plate,  into 
which  a  wire  may  be  hooked. 

The  vessel  must  be  closed  while  warm,  dampness  being  fatal  to  all 
electrical  experiments.  Hence,  such  instruments  are  sometimes  dried 
artificially  by  introducing  calcium  chloride,  a  compound  which  ab- 
sorbs the  moisture  of  the  air. 

Electrification  by  Contact. — Let  a  ball,  A,  supported 
on  a  stem  of  hard  rubber  or  glass,  be  connected  with  the 

electroscope  by  a  metal- 
lic wire  (see  Fig.  326). 
Excite  a  glass  tube,  a 
stick  of  sealing-wax,  or 
a  wooden  ruler,  by  fric- 
tion with  flannel,  silk, 
or  a  cat's  skin,  and 
bring  it  in  contact  with 
the  ball.  The  gold  leaves 
of  the  electroscope  at 
once  diverge,  showing 
that  they  repel  each 
other.  Touch  A  with  the  hand  and  they  collapse.  The 
electrification  has  disappeared. 

If  the  wire  be  replaced  with  a  silk  thread  or  a  glass  tube,  no  effect 
will  be  produced  when  A  is  touched  with  the  excited  body ;  but  the 
leaves  will  diverge  if  the  latter  be  brought  in  contact  with  the  electro- 
scope disk.  This  shows  that  a  silk  thread  or  glass  rod  does  not  con- 
duct electricity.  If  the  thread  be  wet,  it  behaves  like  a  metal  wire, 
but  conducts  more  and  more  imperfectly  as  it  dries. 

Insulation. — A  body  like  A,  mounted  wholly  on  non- 
conductors, is  said  to  be  insulated.  A  piece  of  metal  held 
in  the  hand  can  not  apparently  be  electrified,  because  the 
electricity  is  conducted  away  through  the  body. 

Stroke  the  ball  A  with  a  cat's  skin  while  it  is  connected 
with  the  electroscope  by  a  conductor.  Stand  on  an  insulat- 
ing stool,  consisting  of  a  dry  pine  board  supported  upon 
four  tumblers  or  four  small  cakes  of  parafnne.  Touch  the 


FIG.  326.— ILLUSTRATING  ELECTRIFICATION  BY 
CONTACT,  AND  THE  CONDUCTING  POWER  OF 
DIFFERENT  BODIES. 


INDUCTION.  443 

electrified  knob  or  the  electroscope.  The  leaves  will  fall 
somewhat  together,  but  remain  permanently  deflected  if 
you  are  well  insulated. 

If  tumblers  are  used,  they  may  have  to  be  warmed,  or 
perhaps  exchanged  for  others,  as  some  glass  is  not  a  good 
insulator.  In  touching  the  knob,  you  cause  the  charge  on 
the  knob  and  leaves  to  diffuse  itself  in  part  over  your  body. 

Provide  two  insulating  stools,  and  let  a  person  standing  on  one 
stroke  the  hand  of  a  companion  on  the  other  with  a  cat's  skin.  Both 
persons  will  become  electrified,  the  first  positively  and  the  other  nega- 
tively. This  distribution  of  the  charges  can  be  tested  by  the  electro- 
scope. If  the  instrument  has  been  charged  by  contact  with  an  excited 
glass  rod  rubbed  with  silk,  the  hand  of  a  positively  charged  person 
brought  near  the  electroscope  disk  will  cause  the  leaves  to  diverge  more 
widely.  To  test  the  negative  charge  on  the  other  person,  the  electro- 
scope should  be  charged  by  contact  with  hard  rubber  or  gutta-percha 
rubbed  with  flannel  or  a  cat's  skin.  The  leaves  will  again  be  repelled 
more  widely.  If  the  electroscope  is  electrified,  a  body  oppositely 
charged,  on  being  presented,  will  cause  the  leaves  to  fall  together; 
but,  as  an  unelectrified  body  would  cause  the  leaves  to  behave  in  the 
same  manner,  the  repulsion  of  the  leaves  is  always  the  safe  test. 

Electrification  by  Induction. — Suppose  two  insulated 
balls,  A  and  B,  to  be  placed  in  contact  with  each  other,  as 
in   Fig.   327.     Rubber 
balls,  covered  with  gold- 
leaf  or  tin-foil,  or  even 
two  apples,  will  answer 
the   purpose.       If   ap- 
ples are  used,  they  must 
be  mounted  on  a  rod, 
or  a  tube  sealed  at  the 
end  to  keep  out  moist- 
ure,    Or     they    may    be      Fio.  327.— ILLUSTRATING  ELECTRIFICATION  BY 
hung  on  silk  cords. 

Bring  an  electrified  body,  C,  near  one  of  the  balls,  as 
shown.  Now  move  A  away,  while  C  remains  in  position. 
Both  A  and  B  will  be  found  to  be  electrified.  The  opposite 


444  ELECTRICITY. 

electricity  appears  to  have  been  attracted  to  the  nearer  ball, 
and  the  like  electricity  repelled  to  the  more  distant  one.  If 
the  electricity  of  the  inducing  body  C  is  reversed  in  sign, 
the  charges  on  A  and  B  will  be  reversed  likewise. 

When  a  body  is  thus  electrified  by  means  of  another 
electrified  body,  without  contact,  it  is  said  to  be  electrified 
by  induction. 

Discharge  A  and  B  by  touching  them,  and  again  bring  C  to  the 
position  shown  in  Fig.  327.  The  two  bodies  aro  again  charged.  Next 
remove  C,  and  afterward  test  A  and  B.  They  will  be  found  neutral. 

While  the  bodies  are  all  in  the  position  shown  in  Fig.  327,  touch 
either  A  or  B  with  the  hand.  A  feeble  spark  will  be  felt.  Remove 
the  hand,  and  the  two  bodies  A  and  B  will  seem  neutral  in  the  presence 
of  C.  If  C  is  removed,  the  two  bodies  will  be  found  charged  with  elec- 
tricity the  opposite  of  that  on  C.  When  the  body  was  touched  by  the 
hand,  the  repelled  electricity  escaped  to  the  ground,  through  the  per- 
son of  the  experimenter.  The  attracted  charge  was  held  or  bound  by 
the  opposite  charge  on  C.  When  the  body  C  was  removed,  the  bound 
charge  on  A  and  B  became  a  free  charge.  It  would  then  go  to  the 
earth  if  received  by  the  hand. 

The  Electroscope  is  best  charged  by  Induction. — 

Bring  an  electrified  body — a  glass  rod,  for  instance — near 
the  instrument.  The  negative  electricity  will  be  attracted 
to  the  plate,  and  the  positive  electricity  will  be  repelled  to 
the  leaves,  which  will  diverge.  Touch  the  plate,  and  the 
leaves  will  collapse  as  the  repelled  electricity  upon  them 
escapes.  Now  remove  the  inducing-rod.  The  leaves  again 
diverge  as  the  attracted  electricity  is  diffused  over  them. 

There  remains  a  free  charge  .on  the  electroscope  leaves, 
having  the  opposite  sign  from  that  contained  on  the  induc- 
ing body.  If  the  inducing-rod  be  now  brought  up  toward 
the  electroscope,  the  leaves  will  again  collapse.  Any  posi- 
tively-charged body  will  produce  the  same  effect ;  but  a 
negatively-electrified  body  will  cause  the  leaves  to  diverge 
more  widely,  as  more  electricity  is  repelled  to  the  leaves. 

The  Electroph'orus  is  a  device  for  the  electrification 
of  a  body  by  induction.  Into  a  shallow  dish  of  metal  pour 


THE  ELECTROPHORUS. 


melted  sealing-wax,  making  the  surface  of  the  layer  as  level 
as  possible.  To  the  center  of  a  somewhat  smaller  metal  disk, 
fasten  a  handle  of  glass.  Avoid  sharp  edges  on  the  disk^* 

Stroke  the  sealing-wax  with  a  cat's  skin  or  a  raccoon's  tail,  so  as  to 
electrify  it  negatively.     Place  the  disk  upon  the  excited  wax,  and  its 

neutral   electricity  will    at     

once  be  decomposed  by  in- 
duction, the  lower  surface 
being  positively  and  the  up- 
per surface  negatively  elec- 
trified. Touch  the  disk  with 
the  finger,  so  that  its  nega- 
tive electricity  may  be  con- 
ducted away.  Then  lift  the 
disk  by  the  insulating  han- 
dle, and  it  will  be  found 
sufficiently  charged  with 
positive  electricity  to  yield 
a  spark  when  the  knuckle  is 
presented.  The  spark  will 
ignite  gas  from  a  Bunsen 
burner,  if  the  burner  is  con- 
nected with  the  gas-pipe  by 
a  metal  wire.  These  experi- 
ments may  be  repeated 
several  times,  in  favorable  weather,  without  freshly  rubbing  the  wax. 

Instead  of  touching  the  finger  to  the  disk,  as  in  Fig.  328,  the  point 
of  a  sewing-needle  held  in  the  hand  may  be  brought  near  it. 

QUESTIONS.— Describe  the  gold-leaf  Electroscope.  In  what  way  is  dampness  ex- 
cluded ?  How  may  it  be  charged  by  contact  ?  How  positively  ?  How  nega- 
tively ?  When  is  a  body  said  to  be  insulated  ?  Describe  an  insulating  stool ; 
an  experiment  by  which  two  persons  on  insulating  stools  may  be  charged  with 
positive  and  negative  electricity.  Why  can  you  not  depend  on  the  collapse  of 
the  gold  leaves  in  determining  the  electrical  state  of  a  body  brought  near  the 
electroscope  ? 

Explain  fully  electrification  by  Induction.  How  may  you  charge  the  electroscope 
by  induction  ?  If  it  is  charged  negatively  and  an  insulated  brass  ball  is  brought 
near,  what  is  the  electrical  condition  of  the  ball  when  the  leaves  slightly  col- 
lapse ?  When  they  slightly  diverge  ?  Suppose  two  insulated  metal  balls  to  be 
placed  in  contact,  and  a  positively-electrified  glass  rod  to  be  brought  near  one, 
and,  while  it  is  in  position,  remove  the  other.  Then  remove  the  glass  rod.  On 


FIG.  328. — THE  ELECTROPHORUS. 


*  Any  tinner  can  furnish  the  requisites  for  a  cheap  electrophorus. 


446  ELECTRICITY. 

bringing  the  balls  near  to  each  other  again,  a  spark  will  pass  between  them. 
Give  the  reason.  Explain  the  action  of  the  Electrophorus.  Place  a  pith-ball  on 
a  metal  plate  provided  with  a  glass  handle  ;  then  place  the  plate  on  a  cake  of 
resin  which  has  been  rubbed  with  a  cat's  skin.  When  the  plate  is  touched  with 
the  finger  and  then  lifted  by  the  handle,  the  pith-ball  jumps  off.  Why  ?  What 
must  you  do  in  order  to  get  a  succession  of  sparks  from  the  electrophorus  ? 


ELECTRICAL  MACHINES  AND  CONDENSERS. 

Electricity  confined  to  the  Surface.  —  No  electricity 
exists  on  the  inner  surface  of  a  conducting  shell.  In  Fig. 
329  an  insulated  cylinder  of  wire  gauze  is  represented  as 
electrified  and  as  repelling  the  pith- 
balls  hung  on  the  outside.  Those  on 
the  inside  are  not  affected. 

A  metal  ball  hung  on  a  silk 
cord,  if  brought  in  contact  with 
the  outside  of  the  electrified  wire 
screen,  receives  a  charge,  as  is  shown 
by  its  effect  on  the  electroscope.     If  the 
wire  screen  is  made  large  enough  to  admit 
an  experimenter  with  the  electroscope,  it 
is  found  that,  by  bringing  the  testing-ball 
in  contact  with  the  inside  of  the  screen,  no 
charge  is  obtained.     If  the  ball,  charged  by 
contact  with  the  outer  surface,  is  carried 
inside  and  placed  in  contact  with  the  inner 
surface  of  the  screen,  its  whole  charge  goes    FlG-  SSQ.-INSULATED  CYLIN- 
,,  ,         „  DER   OF   WIRE    GAUZE, 

to  the  external  surface.  PITH-BALLS. 


Electricity  may  be  attracted  to  the  in- 
ner surface  of  a  hollow  ball  by  a  charge  upon  an  insulated  body  with- 
in the  cavity  (see  Fig.  343).  If  the  body  makes  contact  inside  the 
cavity,  the  charge  escapes  to  the  surface. 

The  principle  explained  above  is  practically  applied  in  a 
variety  of  so-called  electrical  machines,  contrivances  for  de- 
veloping and  collecting  large  quantities  of  statical  electricity, 
or  electricity  produced  by  friction. 

In  the  Induction-Machine  is  utilized  the  principle  of 
electrification  by  induction. 


INDUCTION  MACHINE. 


447 


One  form  is  shown  in  Fig.  330.  Here  I  I  are  inductors, 
supposed  to  be  at  different  potentials.  They  have  the  form 
of  hemi-cylindrical  shells.  The  hollow  metal  balls  a  and  a', 
called  carriers,  are  mounted  on  the  ends  of  radial  insulating 


FIG.  330. — INDUCTION  ELECTRIC  MACHINE. 

rods,  and  revolve  around  a  vertical  axis.  As  the  balls  sweep 
through  the  concave  inductors  they  are  momentarily  placed 
in  metallic  contact  with  one  another  by  means  of  springs 
mounted  on  rods,  b  b,  which  are  connected  by  a  wire.  The 
repelled  charges  of  opposite  sign  cancel  each  other  by  being 
added  together  on  these  rods.  As  the  carriers  move  on  to 
the  positions  a  a,  each  will  have  a  free  charge,  opposite  in 
sign  from  that  on  the  inductor  which  it  has  just  left. 

The  balls,  a  #,  next  pass  inside  of  the  collectors,  C  C, 
where  they  touch  a  metal  spring,  by  means  of  which  their 
charges  are  wholly  carried  to  the  external  surfaces  of  C  C. 
The  carriers,  when  in  the  position  a'  #',  are  therefore  neu- 
tral, and  the  same  operation  is  repeated.  Each  collector  is 
connected  by  means  of  a  wire,  w,  with  the  inductor  toward 
which  the  carrier  moves. 


448 


ELECTRICITY. 


There  will  always  be  such  a  difference  of  potential  between  the  two 
sets  of  conductors  in  this  machine  that,  when  the  carriers  are  turned, 
the  electrification  will  begin  and  will  increase  until  the  leakage  in  a 
second  equals  the  amount  added.  If,  several  hours  after  you  have 
brushed  your  clothing,  you  should  stand  nearer  to  one  side  of  the  ma* 
chine  than  to  the  other,  this  will  be  enough  to  cause  it  to  excite  when 
turned.  When  the  machine  is  to  be  used  for  producing  sparks,  each 
rod  of  the  universal  discharger  (see  page  460)  must  be  connected  with 
one  of  the  wires,  w  w. 

In  Sir  William  Thomson's  Water-dropping  Elec- 
tric Machine,  two  jets  of  water,  J,  from  any  common 
source,  H,  fall  through  two  hollow  cylindrical  inductors,  ] 
(see  Fig.  331).  The  jets  are  controlled 
by  screw- clamps,  so  that  they  break  into 


FIG.  331. — WATER-DROPPING  INDUCTION-MACHINE. 


FIG.  333. 


drops  half-way  through  the  inductors,  as  shown  in  vertical 
section,  Fig.  332. 

There  is  always  sufficient  difference  of  potential  between 
the  two  inductors  to  start  the  machine  when  the  water  be- 
gins to  drop.  In  the  inductor  which  is  negative  with  respect 
to  the  other,  the  jet  forms  a  conductor,  the  nearest  end  of 
which  is  positively  electrified  by  induction.  The  negative 
charge  is  repelled  up  the  jet,  and  the  drops  fall  away  posi- 


ACTION   OF   POINTS. 


449 


tively  electrified  into  a  funnel  on  the  inside  of  the  collector 
below.  Here  they  lose  their  whole  charge,  which  goes  to 
the  external  surface.  The  positively-charged  collector  is 
connected  with  the  inductor  on  the  other  support  by  means 
of  a  wire,  w.  This  inductor  acts  precisely  like  its  com- 
panion, a  change  of  sign  only  being  required  for  the  explan- 
ation. 

The  drops  of  water  constitute  the  carriers.  On  each  side,  the  drops 
are  falling  away  from  an  inductor  which  attracts  them,  and  toward  a 
collector  which  repels  them.  They  also  repel  one  another ;  hence  a 
large  part  of  them  fall  outside  of  the  collectors.  A  difference  of  po- 
tential of  about  7,000  volts  (see  page  493)  can  easily  be  maintained  by 
this  device,  as  long  as  the  water-supply  is  kept  up. 

The  supporting  columns  may  be  made  from  heavy  glass  tubing. 
The  inductors  should  be  about  an  inch  and  a  half  in  diameter,  and 
three  or  four  inches  in  length.  The  whole  apparatus  can  be  made  by 
the  pupil  with  the  aid  of  a  tinner,  and  affords  a  most  instructive  illus- 
tration of  many  of  the  phenomena  of  electricity. 

Action  of  Points. — If  an  insulated  cylinder  of  brass, 
having  rounded  extremities,  be  connected  with  an  electric 

machine,  and  a  test-ball 
be  then  applied  at  differ- 
ent  parts  of  the  surface 
of  the  cylinder,  the  ball 
will  be  found  most  strong- 
ly charged  when  applied 
at  the  ends.      It  will  then  affect  most 
forcibly  the  gold  leaves  of  the  electroscope. 

If  the  conductor  have  the  form  shown  in  Fig. 
334,  a  testing  sphere  applied  to  the  pointed  ex- 
tremity will  acquire  a  greater  charge  than  at  the 
rounded  end,  the  least  charge  being  acquired  when 
contact  is  made  at  the  side.  The  density  of  the 
charge  is  said  to  be  greatest  at  the  ends.  If  the  electrified  body  ter- 
minates in  a  sharp  point,  as  in  Figs.  335  and  336,  the  density  is  so 
great  that  the  electricity  escapes  from  the  point  very  rapidly  and  the 
body  becomes  neutral.  In  the  dark,  the  point  appears  tipped  with  a 
luminous  glow  called  a  brush. 


FIG.  334. 


450 


ELECTRICITY. 


Should  the  flame  of  a  candle  be  held  in  front  of  the  point,  it  will 
be  blown  aside,  because  the  particles  of  air  in  the  immediate  vicinity 
of  the  point,  having  become  electrified  by  contact,  are 
repelled  by  the  highly  charged  point  with  such  veloci- 
ty as  to  drive  back  the  flame  in  turn. 

The  mutual  repulsion  between  points  free  to  move 
and  the  electrified  air  which  flows  from  them,  is  illus- 
trated by  the  electric  whirl  or  flier,  consisting  of  metal- 
lic wires  branching  out  from  a  common  center,  and 
with  pointed  ends  bent  in  the  same  direction.  If  the 
whirl  is  balanced  on  a  rod  attached  to  the  conductor 
of  an  electric  machine  in  action,  it  will  revolve  in  a  direction  opposite 
to  that  in  which  the  bent  wires  point.  Why?  When  the  room  is 
darkened,  the  points  become  luminous,  and  a  circle  of  fire  seems  to  be 
formed. 

The  faint  glow  known  as  St.  Elmo's  fire,  sometimes  seen  tipping 
the  extremities  of  masts,  bayonets,  and  even  the  ears  of  horses,  partic- 


FIG.  335.— ELEC- 
TRIC BRUSH. 


z 


FIG.  336.— CANDLE-FLAME  REPELLED 
BY  ELECTRICITY  FROM  POINTS. 


FIG.  337.— ELECTRIC  WHIRL. 


ularly  during  thunder-storms,  is  electricity  slowly  discharging  itself 
from  or  into  pointed  bodies. 

This  action  of  points  is  utilized  in  some  forms  of  electrical  ma- 
chines, now  to  be  described.  The  conductors  of  all  electrical  machines 
terminate  in  rounded  ends  or  edges,  in  order  to  avoid  leakage.  They 
should  be  kept  free  from  dust,  as  brush  discharges  are  likely  to  stream 
even  from  dust-particles. 

The  Toepler-Holtz  Machine,  a  celebrated  generator 
of  electricity  both  for  medical  purposes  and  physical  use 
(see  No.  3,  page  435),  is  really  a  combination  of  two  in- 
duction-machines like  that  described  on  page  447.  On  the 


PRINCIPLE  OF  THE  TOEPLER-HOLTZ  MACHINE. 


back  of  a  stationary  glass  plate  (Fig.  338)  are  two  cards,  X 
X,  which  act  as  inductors  ;  and  on  a  smaller  revolving  glass 
plate,  in  front  of  the  former,  are  pasted  a  series  of  carriers, 
a  a',  made  of  tin-foil,  each  of  which  has  in  its  center  a 
metal  button  or  stud  designed  to  serve  as  a  contact.  As  the 


FIG.  338.— PRINCIPLE  OF  THE  TOEPLER-HOLTZ  MACHINE. 

carriers  are  ahout  to  leave  the  inductors,  the  two  on  the 
same  diameter  are  touched  by  flexible  metal  springs  or  wire 
brushes  fixed  to  the  stationary  diagonal  rod  #,  which  crosses 
the  moving  plate.  The  repelled  charges  on  the  carriers  are 
thereby  simultaneously  removed,  exactly  as  is  done  by  the 
rods  I  I  in  Fig.  330. 

Passing  to  the  opposite  inductor,  each  carrier  touches  a  second 
metal  brush  in  contact  with  that  inductor  through  rods  C  C.  The 
bound  charge  which  each  carrier  held  at  the  previous  contact  with  the 
diagonal  rod  b,  while  in  front  of  the  other  inductor,  is  now  in  part 
communicated  to  the  inductor  having  a  like  charge,  through  the  col- 
lectors C  C.  The  function  of  these  carriers  is  to  restore  the  charges 
which  leak  away  from  the  two  inductor-cards,  the  operation  being  ex- 


452  ELECTRICITY. 

actly  like  that  shown  in  Fig.  330.  One  of  the  cards  is  thus  rapidly 
replenished  with  positive,  the  other  with  negative,  electricity. 

As  the  inductors  become  charged,  they  act  inductively  on  the  re- 
volving plate,  electricity  of  the  like  sign  being  repelled  to  the  surface* 
farthest  from  the  card  inductor.  The  combs  C'  are  also  acted  upon 
inductively,  and  electricity  of  the  opposite  sign  from  that  on  the  card 
is  attracted,  and  streams  from  the  points  of  the  combs  in  a  brush  dis- 
charge upon  the  plate.  When,  for  instance,  any  part  of  the  glass  in 
its  revolution  arrives  at  the  comb  C'  on  the  right,  the  negatively- 
charged  glass  around  the  collector  is  rendered  neutral  by  an  attracted 
brush  discharge  from  the  comb,  which  leaves  a  repelled  or  free  nega- 
tive charge  on  the  conductor.  These  conductors  terminate  in  knobs, 
K  K,  between  which  a  discharge  of  sparks  is  thus  kept  up  while  the 
glass  plate  is  in  revolution.  In  the  second  half  of  a  revolution,  the 
operations  are  all  repeated,  the  signs  of  the  charges  being  reversed. 

The  action  of  the  Toepler-Holtz  machine  is  the  same  as  that  of 
the  electrophorus. 

The  Friction  Electric  Machine,  the  oldest  form,  but 
far  inferior  to  the  modern  induction-machines  as  a  producer 
of  electricity,  is  a  simple  contrivance  for  rubbing  glass  and 
silk  or  leather  together,  and  collecting  the  electricity  gener- 
ated. One  form  consists  of  a  circular  plate  of  glass,  A  (see 
Fig.  339),  which  may  be  revolved  between  cushions,  D, 
coated  with  an  amalgam  (usually  composed  of  zinc,  tin,  and 
mercury,  mixed  with  grease).  When  the  plate  is  revolved, 
the  lower  part  becomes  positively  electrified.  The  electricity 
is  collected  by  the  comb  F  and  carried  to  the  prime  con- 
ductor P,  which  is  mounted  on  a  glass  column  or  fixed, 
insulated,  to  the  stand  of  the  machine.  The  clamp  at  the 
same  time  receives  an  equal  negative  charge,  which  is  com- 
municated to  a  second  insulated  conductor,  N.  The  silk 
apron,  S,  in  a  measure  prevents  leakage. 

Connect  P  and  N  by  a  wire.  They  will  both  remain  neutral,  or  at 
the  same  potential  as  the  earth.  Insulate  them  from  the  earth  and 
from  each  other,  and  N  will  become  negatively  charged,  P  positively. 
In  other  words,  the  potential  of  N  sinks  below,  while  the  potential  of 
P  rises  above,  that  of  the  earth.  The  difference  of  potential  is  de- 
pendent on  the  materials  rubbed  together.  A  spark  can  be  drawn 
from  either  conductor  by  any  person  standing  on  the  floor. 


THE  FRICTION-MACHINE. 


453 


Connect  either  P  or  N  with  a  gas  or  water  pipe,  or  a  lightning-rod 
having  a  good  earth  connection.  Even  a  chain  lying  on  the  floor  will 
serve  the  purpose.  This  is  called  "  grounding  "  the  conductor.  Much 
longer  sparks  can  now  be  drawn  from  the  other  insulated  conductor, 
but  none  can  be  obtained  from  the  grounded  conductor.  If  N  has 


FIG.  339.— FRICTION  ELECTRICAL  MACHINE. 

been  grounded,  its  potential  has  been  raised  to  that  of  the  earth ;  but 
the  potential  of  the  positive  conductor  has  been  similarly  raised,  since 
the  difference  in  potential  has  not  been  changed.  The  difference  of 
potential  between  the  earth  and  the  insulated  conductor  is  therefore 
increased.  Sparks  of  the  same  length  may  be  drawn  from  each  con- 
ductor, if  both  are  insulated,  and  a  person,  standing  on  an  insulating 
stool,  touch  either  and  present  his  knuckle  to  the  other. 

A  person  on  an  insulating  stool,  having  once  touched  the  con- 
ductor, receiving  a  spark  as  he  does  so,  may  again  touch  it  without 
receiving  a  spark.  He  is  already  charged  to  the  potential  of  the  con- 
ductor, and  the  electricity  can  not  leak  away.  A  person  on  the  floor 
may  draw  a  spark  from  him  when  thus  charged. 


NOTE.— In  another  form  of  the  friction-machine  a  glass  cylinder  is  used  in- 
stead of  a  circular  plate.  Cylinders  of  glass,  amalgam,  etc..  may  be  purchased 
at  slight  cost  from  instrument-dealers,  and  the  pupil  may  easily  construct  a  sim- 
ple friction-machine  for  himself. 


454 


ELECTRICITY. 


Electrical  Condensers,  or  accumulators,  assume  a  va- 
riety of  forms,  according  to  the  uses  for  which  they  are  de- 
signed. A  common  condenser  is 
the  Leyden  (li'den)  jar,*  which 
may  be  used  with  all  the  forms  of 
electrical  machines  so  far  described, 

The  Ley  den-jar  is  merely  a 
glass  vessel  coated  within  and  with- 
out, for  about  two  thirds  of  its 
height,  with  tin-foil,  put  on  with 
flour-paste.  Through  a  cork  or 
wooden  cover  closing  the  mouth, 
passes  a  metal  rod,  which  termi- 
nates above  in  a  ball  (why?),  and 
from  which  a  chain  hangs  in  con- 
tact with  the  inner  lining  of  the 
jar. 

If  two  such  jars  are  connected  with  the  Holtz  machine,  as  shown 
in  Fig.  341,  the  character  of  the  discharge  between  the  two  terminals 


FIG.  340.— THE  LEYDEN-JAR. 


FIG.  341.— LEYDEN- JARS  IN  CONTACT  WITH  TOEPLER-HOLTZ  MACHINE. 

changes  entirely.     Instead  of  a  continuous  brush  discharge,  accom- 
panied by  a  rustling  and  crackling  sound,  the  discharge  comes  at  inter- 


So  called  because  first  used  at  Leyden,  Holland. 


PRINCIPLE  OF  THE  LEYDEN-JAR. 


455 


vals,  the  length  of  which  increases  with  the  width  of  the  gap  between 
the  knobs,  and  with  the  size  or  number  of  the  jars.  The  electricity 
appears  to  accumulate  until  the  jars  are  charged,  and  then  breaks 
through  the  air  with  a  sound  like  the  crack  of  a  whip.  Immediately 
after  the  spark  has  passed,  the  whole  machine  is  virtually  discharged, 
as  may  be  seen  by  suddenly  stopping  the  revolving  plates  when  the 
spark  passes. 

One  or  more  jars  may  be  used  with  the  Holtz  machine,  by  connect- 
ing all  their  inside  coatings  with  one  another  and  with  one  side  of 
the  machine,  while  the  outside  coatings  are  connected  with  the  other. 
The  connecting  wires  should  have  a  globule  of  solder  upon  their  ends, 
in  order  to  prevent  leakage.  The  jars  should  all  be  insulated. 

Action  of  the  Leyden-jar. — If  two  metal  sheets, 
about  two  feet  in  diameter,  are  hung  up  in  parallel  on  silk 
cords,  they  will  act  as  a  condens- 
er. Two  sheets  of  zinc,  such  as 
are  put  under  stoves,  will  answer 
very  well  if  the  edges  and  cor- 
ners are  smoothed.  It  is  neces- 
sary to  suspend  each  piece  on  two 
cords,  in  order  to  keep  them  in 
position.  The  sheets  may  be  con- 
nected by  means  of  a  fine  wire 
with  the  conductors  of  the  Holtz 
machine,  which  should  already 
have  the  two  Leyden-jars  belong- 
ing to  it  attached. 

It  will  be  found  that,  with  the  same 
speed  of  rotation,  the  sparks  will  come 
less  frequently.  The  metal  plates  will 
be  attracted  together  unless  held  apart 
by  silk  cords  or  other  insulators.  If 
the  distance  between  the  plates  is 
doubled,  the  sparks  will  pass  twice  as  rapidly  between  the  knobs  of  the 
Holtz  machine.  Increasing  the  size  of  the  plates,  or  placing  them 
nearer  together,  increases  the  interval  between  the  sparks.  It  is  also 
said  to  increase  the  capacity  of  the  condenser.  The  greater  the  ca- 
pacity of  the  condenser,  the  longer  the  time  required  for  it  to  become 


FIG.  342.— ILLUSTRATING  ACTION 
OP  LEYDEN-JAR. 


456 


ELECTRICITY. 


charged  with  electricity,  so  that  a  spark  will  break  across  between  the 
knobs  when  placed  a  fixed  distance  apart. 

The  reason  for  the  greater  capacity  of  one  of  the  plates,  when  near 
the  other,  is  due  to  the  attraction  between  the  two  charges  of  opposite 
sign  upon  the  plates.  This  attraction  is  shown  by  the  motion  of  the 
plates  toward  each  other. 

Disconnect  the  plates  from  the  machine,  and  touch  them  alter- 
nately. Only  a  feeble  charge  will  pass  to  the  hand  at  contact.  After 
many  such  alternate  contacts,  if  the  plates  are  touched  simultaneously, 
a  smart  shock  will  be  felt.  When  only  one  plate  is  connected  with  the 
ground  through  the  body,  the  electricity  on  it  can  not  escape,  because 
of  the  attraction  of  the  electricity  on  the  other  plate. 

Another  Form  of  Condenser,  for  experimental  pur- 
poses, is  shown  in  Fig.  343.     It  is  simply  a  hollow  spherical 
conductor,  with  an  opening  cut  in 
the  top.    This  opening  is  closed  by 
a  cover  fitted  with  a  glass  handle, 
and  is  large   enough  to  admit  a 
gilded  rubber  or  hollow  metal  ball, 
which  is  suspended  from  a 
hook  in  the  cover  by  a  fiber 
of  silk.    An  opening  in  the  side  will 
serve  to  admit  a  copper  wire  cov- 
ered with  rubber,  or   a  knitting- 
needle  coated  with  sealing-wax,  to 
be  used  as  a  charger. 

Charge  the  inner  ball  by  means  of  the 
electrophorus  or  either  conductor  of  the 
electrical  machine,  and  remove  the  charg- 
ing-wire.  Suppose  this  charge  to  be 
positive.  Then  a  negative  charge  will 
be  attracted  to  the  inside  of  the  outer 
shell,  while  an  equal  positive  charge  will  be  repelled  to  the  outer  sur- 
face. Lift  out  the  inner  sphere  without  touching  the  outer  shell.  The 
latter  will  be  found  unelectrified,  showing  that  the  two  charges  are 
equal.  Replace  the  charged  sphere.  The  outer  sphere  will  now  appear 
electrified  again,  and  will  affect  the  gold  leaves  of  the  electroscope  if 
the  testing-sphere  connected  with  it  be  brought  near. 

Next  touch  the  outer  sphere  with  the  hand.    The  repelled  charge 


FIG.  343.— SPHERICAL  CONDUCT- 
OR, WITH  INCLOSED  ELECTRI- 
FIED BALL. 


SHIELDING  EFFECT  OF  CONDUCTING  SHELLS.    457 

will  escape,  but  the  two  bound  charges  will  still  remain.  They  exert 
equal  and  opposite  effects  on  the  electroscope.  If  the  silk  fiber  now 
be  broken,  so  as  to  make  contact  within,  the  whole  system  will  instantly 
become  neutral.  This  proves  that  the  induced  charge  on  the  outer 
sphere  is  equal  to  the  inducing  charge  on  the  inner  sphere. 

If  the  spheres  are  neutral,  and  a  charge  is  communicated  to  the 
outer  shell,  no  charge  will  be  induced  on  the  inner  shell.  The  whole 
charge  will  remain  on  the  outer  surface  of  the  outer  shell. 

Act  inductively  upon  the  two  spheres,  one  of  which  incloses  the 
other,  as  was  done  on  the  bodies  A  and  B,  in  Fig.  327.  The  attracted 
electricity  will  be  found  on  the  outer  surface  of  the  outer  shell,  nearest 
the  inducing  body,  while  the  repelled  charge  will  be  on  the  side  farthest 
from  the  inducing  body,  and  also  on  the  outer  surface.  No  electricity 
can  be  found  on  the  inner  ball,  or  anywhere  in  the  interior  cavity. 


FIG.  344. — WIRE  CYLINDER  INCLOSING  ELECTROSCOPE. 


Screening  Effect  of  a  Metallic  Shell. — Any  space 
completely  surrounded  by  a  metallic  or  conducting  shell  is 
30 


458  ELECTRICITY. 

shielded  from  all  electrical  influence  from  without.  This  is 
best  shown  by  setting  a  screen  made  of  common  wire  gauze 
over  the  electroscope,  the  latter  resting  upon  a  metal  sheet. 
Sparks  from  the  electric  machine  may  be  sent  through  the 
wire  netting,  and  electrified  bodies  may  be  moved  about  out- 
side of  the  screen,  without  in  the  least  degree  affecting  the 
gold  leaves.  If  the  screen  and  electroscope  rest  upon  the 
poorly-conducting  table  instead  of  the  metal  sheet,  the  leaves 
are  at  once  affected.  A  powder-house  inclosed  wholly  in  sheet- 
iron,  the  floor  included,  would  be  safe  against  lightning. 

Cause  for  the  Increased  Capacity  of  Condensers. 

— The  small  sphere  of  Fig. 
343  has  a  less  capacity  in 
the  open  air  than  when  sur- 
rounded by  the  concentric 
shell,  because  of  the  attrac- 
tion of   the   opposite  elec- 
tricity induced  on  the  outer 
shell.  The  attracting  charges 
seem  to  bind  each 
other.      The    same 
action   takes    place 
on  the  coats   of   a 
Leyden  -  jar.         A 
sphere      within      a 
room  has  a  greater 
capacity  than  when 
in  the  open  air.  The 
walls  of   the   room 
act  as  the  outer  coating  of 
the  condenser. 

The      Capacity      of     a       FlG-  ^.-INCREASE  OF  CAPACITY  BY 

METALLIC  SHELL. 

Body  for  heat  is  measured 

by  the  amount  of  heat  required  to  raise  its  temperature  one 

degree.     It  will  be  noted  that  the  capacity  is  not  measured 


MEASURE  OF  CAPACITY.  459 

by  the  amount  of  heat  the  body  will  hold.  Any  amount 
of  heat  may  be  added  to  it,  and  the  temperature  will  rise 
with  the  amount  added. 

The  capacity  of  a  body  for  electricity  is  measured  by 
the  amount  of  electricity  required  to  raise  its  potential  by 
unity. 

Suppose  electricity  to  be  added  to  a  body,  A  (Fig.  345),  until  its 
potential  is  raised  to  unity,  that  of  the  earth  being  always  assumed  to 
be  zero.  Now,  suppose  electricity  added  also  to  B  until  no  spark 
would  pass  if  A  and  B  were  momentarily  connected  by  a  fine  insulated 
wire.  Then  A  and  B  are  said  to  be  at  the  same  potential.  Suppose  a 
body,  C,  equal  to  B  in  size  but  surrounded  by  a  grounded  metallic 
shell,  S,  is  also  charged  until  no  spark  passes  when  C  and  A  are  simi- 
larly connected.  The  bodies  A,  B,  and  C,  have  then  all  the  same 
potential. 

It  is  found  that  it  takes  more  electricity  to  charge  C  than  B.  The 
effect  of  the  shell  has  been  to  increase  the  capacity  of  the  inner  body. 
The  capacity  increases  as  the  radial  distance  between  ball  and  shell 
diminishes. 

A  toy  balloon,  coated  with  soot  or  graphite  powder  to  make  it  con 
ducting,  may  be  loaded  to  equilibrium.  If  electrified,  it  will  then  rise. 
The  electrical  forces  make  the  balloon  slightly  larger. 


QUESTIONS.— Prove  that  electricity  is  confined  to  the  outer  surface  of  bodies. 
How  may  it  be  attracted  to  the  inner  surface  of  a  hollow  ball  ?  What  are 
Electric  Machines  ?  Describe  an  induction-machine  in  which  the  inductors 
are  semi-cylindrical  shells ;  Sir  William  Thomson's  water-dropping  machine. 
What  can  you  say  of  the  action  of  points  ?  Define  an  electric  brush.  What 
happens  when  the  flame  of  a  candle  is  brought  near  a  charged  point  ?  Explain 
St.  Elmo's  fire.  How  is  this  action  of  points  utilized  in  electric  machines? 
State  the  effect  of  smooth  and  rough  surfaces  on  the  escape  of  electricity. 

Describe  minutely  the  Toepler-Holtz  Machine,  referring  to  the  illustration  on 
page  451.  Compare  its  action  with  that  of  the  electrophorus.  Describe  the 
plate  electric  machine.  In  this  machine  the  conductor  is  of  rounded  shape  at 
all  parts  except  where  it  comes  nearest  to  the  glass  plate.  Here  it  is  provided 
with  sharp  projecting  points.  Explain  this.  Why  will  not  a  plate  machine 
work  well  in  damp  weather  ?  If  a  silver  tea-pot  be  insulated  and  electrified, 
and  you  touch  it  in  different  places  with  a  penny  fastened  to  the  end  of  a  stick 
of  sealing-wax,  what  part  of  the  pot  will  give  the  greatest  and  what  part  the 
least  quantity  of  electricity  to  the  penny  ?  How  may  you  decide  with  the  help 
of  the  electroscope  ? 

What  are  Electrical  Condensers  ?  Describe  a  Leyden-jar,  and  the  method  of 
charging  it  by  means  of  electric  machines.  Illustrate  its  action  in  the  case  of 
two  sheets  of  zinc.  Prove  that  the  induced  charge  on  an  outer  spherical  con 


460 


ELECTRICITY. 


ductor  is  equal  to  the  inducing  charge  on  an  inner  sphere.  Explain  the  screen- 
ing effect  of  a  metallic  shell  or  wire  cylinder.  Under  what  conditions  would  a 
powder-house  be  safe  from  lightning  ?  What  is  meant  by  the  capacity  of  a 
body  for  heat  ?  For  electricity  ? 


THE  ELECTRICAL  DISCHARGE  AND  ITS  EFFECTS. 

Dischargers. — In  discharging  several  Leyden-jars  con- 
nected so  as  to  act  as  one,  it  is  necessary  to  use  some  form 
of  discharger  to  avoid  a  shock,  for  even  a  slight  shock  might 


FIG.  346.— BATTERY  OF  LEY- 
DEN-JABS  IN  Box  LINED 
WITH  TIN-FOIL. 


FIG.  347.— UNIVERSAL  DISCHARGER. 


cause  the  death  of  a  person  affected  with  heart-disease.* 
Hand-dischargers  are  jointed  conductors  provided  with 
glass  or  rubber  handles  (see  No.  4,  page  435).  In  the  uni- 
versal discharger  (Fig.  347),  the  two  conductors  are  sup- 
ported on  glass  columns,  to  which  they  are  hinged  so  that 


*  An  interesting  incident  is  related  in  connection  with  the  experiments  that 
led  to  the  invention  of  the  Leyden-jar.  Prof.  Van  Musschenbroek  (mus'Tcen- 
brddk),  of  Leyden,  observing  that  excited  bodies  soon  lose  their  electricity  in  the 
air,  determined  to  see  whether  he  could  not  collect  and  insulate  the  electricity  in 
a  vessel  of  non-conducting  glass,  so  that  it  might  be  kept  locked  up,  as  it  were, 
ready  for  use.  Accordingly,  he  introduced  a  wire  from  the  conductor  of  an  elec- 
tric machine  into  a  bottle  filled  with  water.  After  the  machine  had  been  working 
some  time,  an  attendant,  holding  the  bottle  in  one  hand,  attempted  to  withdraw 
the  wire  with  the  other,  when  he,  of  course,  received  a  shock,  so  unexpected  and 
so  unlike  anything  he  had  ever  felt  before,  that  it  filled  him  with  consternation. 
Van  Musschenbroek  himself  subsequently  took  a  similar  shock,  which  he  de- 
scribed in  a  letter.  He  says  that  he  felt  himself  struck  in  his  arms,  shoulders, 
and  breast,  so  that  he  lost  his  breath,  and  it  was  two  days  before  he  recovered 
from  the  effects  of  the  blow  and  the  fright.  He  would  not,  he  adds,  take  a  sec- 
ond shock  for  the  whole  kingdom  of  France.  The  shock  of  a  powerful  battery 
will  kill  a  man  and  fell  an  ox ;  even  moderate  discharges  prove  fatal  to  birds 
and  the  smaller  animals. 


EFFECTS  OF  ELECTRIC  SPARK. 


461 


they  may  be  placed  in  any  position.  A  glass  table  between 
serves  to  support  and  insulate  the  body  upon  which  experi- 
ment is  to  be  made. 

Effects  of  the  Electric  Spark — The  effect  of  the 
discharge  from  any  given  jar  or  combination  of  jars  depends 
on  the  nature  of  the  body  through  which  the  discharge 
takes  place.  Bad  conductors  are  shattered.  Good  con- 
ductors, if  sufficiently  large,  are  not  apparently  affected. 
All  bodies  are  heated,  so  that  a  fine  metal  wire  may  become 
warm  or  may  even  fuse. 

Place  a  piece  of  dry  sole-leather  or  a  book  between  the  knobs  of 
the  Holtz  machine,  and  a  hole  may  be  made  in  it  by  the  spark.  Thin 
glass  may  be  pierced  in  a  similar  way.  This  shows  that  the  medium 


FIG.  348. — PUNCTURE  OF  GLASS  BY  ELECTRIC  SPARK. 

between  the  knobs  is  in  a  condition  of  stress,  which  may  produce  a 
rupture  of  the  intervening  body.  Some  idea  of  the  force  exerted  may 
be  obtained  by  pushing  a  punch  through  the  leather  or  book. 

If  you  desire  to  pierce  a  thin  plate  of  glass,  you  may  support  it  on  a 
tumbler,  as  shown  in  Fig.  348.    Bore  a  hole  through  the  bottom  of  the 


462  ELECTRICITY. 

tumbler  with  the  freshly  broken  end  of  a  round  file,  moistened  with  a 
paste  made  of  camphor-gum  and  spirits  of  turpentine.  Let  the  tum- 
bler rest  on  a  sheet  of  tin-foil,  in  contact  with  a  metal  rod  which 
passes  up  through  it  and  ends  in  a  sharp  point  in  contact  with  the 
glass.  Support  an  insulated  rod  above,  terminating  in  a  point  exactly 
on  the  opposite  side  of  the  glass,  which  should  be  washed  clean  with 
soap  and  dried  before  a  fire.  A  little  oil  may  be  poured  on  its  upper 
face  to  keep  moisture  away.  For  a  single  jar,  the  glass  must  be  very 
thin.  If  the  spark  passes  around  the  glass,  it  is  useless  to  repeat  the 
experiment  with  the  same  plate.  Plates  of  glass  2J  inches  thick  have 
been  pierced  by  sparks  from  a  powerful  induction-coil  (see  page  518). 

The  Discharge  in  Rarefied  Gases. — In  the  Geissler 
tube,  platinum  wires  are  sealed  through  the  extremities 
into  chambers,  which  communicate  with  each  other  through 
a  tube  of  glass  bent  into  various  fanciful  shapes.  A  spark 
passing  from  one  wire  to  the  other  must  traverse  this  bent 
tube.  If  the  gas  within  is  at  atmospheric  pressure,  the 
spark  will  pass  around  the  entire  tube  rather  than  through 
it.  If  the  gas  is  pumped  out,  electricity  will  begin  to  flash 
through  the  tube  when  the  terminal  wires  are  in  connection 
with  the  knobs  of  the  Holtz  machine.  As  the  exhaustion 
proceeds,  the  electricity  will  finally  pass  in  a  continuous, 
flickering,  noiseless  discharge,  revealed  by  a  beautiful  glow 
of  light  when  the  experiment  is  made  in  a  dark  room. 

If  the  exhaustion  is  made  more  complete,  the  discharge  is  less 
brilliant,  and  finally  will  cease  altogether.  In  the  highest  attainable 
vacuum,  no  spark  will  pass.  At  a  certain  pressure  the  discharge  takes 
place  most  easily ;  the  insulating  power  of  the  air  is  least.  The  tubes 
are  sealed  at  this  pressure.  A  nearly  perfect  vacuum  thus  implies 
high  insulation ;  a  partial  vacuum  is  a  good  conductor. 

The  Discharge  in  Air — Lightning. — When  the  termi- 
nals of  the  Holtz  machine  have  Leyden-jars  attached,  the 
electricity  accumulates  in  the  jars,  and  the  electrical  stress 
between  the  knobs  increases,  until  finally  the  air  ruptures, 
as  does  the  glass  plate.  Against  the  pressure  of  the  atmos- 
phere, a  long  rarefaction  similar  to  that  of  the  Geissler  tube 
forms  between  the  knobs,  through  which  the  whole  charge 


LIGHTNING-FLASHES.  463 

of  the  jars  passes.  This  is  why  the  jars  and  machine  are 
almost  wholly  discharged  just  after  the  spark  has  passed. 
It  is  as  if  the  knobs  had  been  momentarily  connected  by  a 
fairly  good  conductor. 

Along  the  line  of  the  discharge,  the  air-particles  are  thrown  into  a 
state  of  intense  vibration— they  become  extremely  hot.  They  also 
give  off  a  light,  which  yields  a  spectrum  characteristic  of  the  gas  as 
well  as  of  the  terminals  between  which  the  spark  passes.  This  shows 
that  some  of  the  metal  composing  the  terminals  is  vaporized. 
*  The  pressure  of  the  atmosphere  quickly  closes  the  rarefaction 
with  a  sound,  which  in  large  sparks  like  lightning  is  called  a  crash. 
The  slight  discharge  of  a  Leyden-jar  sounds  like  the  crack  of  a  whip, 
which  is  also  due  to  the  closing  up  of  a  hole  in  the  air. 

The  Lightning-Flash. — The  thunder-cloud  and  the 
earth  constitute  a  huge  condenser.  The  cloud  is  usually 
positively  charged,  and  the  opposite  or  negative  electricity 


FIG.  349.— LIGHTNING-FLASHES,  FROM  INSTANTANEOUS  PHOTOGRAPHS. 


is  induced  upon  the  surface  of  the  earth.  If  the  charges 
accumulate  sufficiently,  a  spark  will  pass  in  a  flash  of  light- 
ning, illustrated  in  the  accompanying  photographs.  It  will 
be  seen  that  the  path  of  lightning  is  not  zigzag  in  shape,  as 
popularly  supposed.  In  one  of  the  pictures  is  apparent  the 
beautiful  branching  effect  often  secured  on  sensitive  plates. 

Protection  against  Lightning. — There  can  be  no 
doubt  of  the  value  of  a  properly  constructed  lightning-rod. 
Before  the  ships  of  the  English  navy  were  armed  with  con- 


464  ELECTRICITY. 

ductors,  frightful  disasters  from  lightning  were  not  uncom- 
mon. They  ceased  with  the  introduction  of  the  copper 
strips  which  Sir  W.  Snow  Harris  designed  for  attachment 
to  the  masts.  The  lightning-rod  is  intended  to  create  a 
line  of  least  resistance,  along  which  the  discharge  must  take 
place  without  damage. 

Lightning-rods  should  rise  in  the  air  as  high  as  chim- 
neys, for  otherwise  the  soot  of  the  chimneys  may  lead  the 
discharge  into  the  house.  The  rods  should  not  usually  he 
higher  than  the  highest  points  to  be  protected,  as  it  is  bet- 
ter not  to  attract  the  lightning,  but  to  have  it  strike  away 
from  the  house  entirely.  The  region  protected  by  a  rod  is 
approximately  a  cone,  whose  height  is  the  rod  and  whose 
base  has  a  radius  equal  to  the  height  of  the  rod. 

A  lightning-rod  should  be  without  joints ;  or  if  jointed,  the  lengths 
should  lap  several  inches  and  be  tightly  wound  with  copper  wire.  The 
rod  should  extend  into  the  ground  until  earth  is  reached  which  is 
always  moist.  It  is  well  to  dig  a  hole  several  feet  deep,  and  fill  around 
the  rod  with  powdered  coke  or  charcoal.  Two  ground  connections  at 
opposite  ends  of  the  building  are  much  better  than  one. 

Thunder. — One  end  of  the  path  of  a  lightning-stroke 
may  sometimes  be  as  much  as  two  miles  farther  from  the 
ear  than  the  other.  The  passage  of  the  discharge  is  prac- 
tically instantaneous  ;  but  as  sound  travels  only  at  the  rate 
of  eleven  hundred  feet  a  second,  the  duration  of  this  thun- 
der will  be  over  nine  seconds. 

The  path  of  the  discharge  is  sometimes  through  air 
which  is  not  acoustically  homogeneous.  The  sound  from 
some  parts  of  the  path  is  so  refracted,  reflected,  or  quenched 
by  interference,  that  the  thunder  is  barely  heard  for  a  sec- 
ond or  more ;  then  it  bursts  into  a  roar  as  sound  from  other 
parts  of  the  path  reaches  the  ear  without  meeting  such  ob- 
struction. The  roar  may  at  this  time  also  be  re-enforced 
by  sound  from  nearer  points  of  the  path,  which  has  been  re- 
flected to  the  ear  after  having  traversed  an  indirect  route. 
The  effect  is  not  unlike  the  rumble  of  a  distant  railway-train 


MAGNETIZING  EFFECT  OF  THE  SPARK.          405 

passing  through  cuts,  tunnels,  or  groves  of  trees,  and  then 
out  into  an  open  stretch  of  track. 

Duration  of  Light ning-Flashes. — We  have  shown 
that  the  duration  of  a  lightning-flash  is  about  the  hundred- 
thousandth  part  of  a  second.  It  seems  to  be  longer  than 
this,  because  of  the  persistence  of  sensations  on  the  retina. 
Falling  rain-drops  at  night,  when  illuminated  by  lightning, 
seem  to  be  stationary  in  the  air.  They  do  not  appreciably 
move ;  even  the  most  rapidly  rotating  bodies  appear  to  be 
perfectly  still  while  illuminated. 

A  jet  of  water  will  show  similar  results  when  illuminated  by  the 
spark  of  a  Leyden-jar.  In  a  dimly  lighted  room,  the  carriers  on  the 
Toepler-Holtz  machine  show  as  a  hazy  ring  upon  the  rapidly  revolv- 
ing plate.  When  the  spark  passes  between  the  knobs,  they  seem  sharp- 
ly defined  and  stationary.  Similar  experiments  may  be  made  with 
Newton's  disk  of  colored  sectors,  or  the  spokes  of  a  revolving  wheel. 

The  Aurora  is  a  luminous  appearance  believed  to  be 
of  electrical  origin.  While  it  is  not  yet  fully  understood, 
all  observations  point  to  the  conclusion  that  it  may  be  re- 
ferred to  electrical  discharge  in  the  upper  and  thinner  por- 
tions of  the  atmosphere. 

Magnetizing  Effect  of  the  Spark. — It  was  early  no- 
ticed by  mariners  that  a  lightning  discharge  often  deranges 
or  reverses  the  magnetism  of  the  compass-needle,  so  that 
the  end  previously  pointing  north  would  point  south. 

The  same  effect  can  be  produced  with  the  comparatively 
feeble  charge  of  a  Leyden-jar. 

Let  the  spark  be  led  around  a  coil  of  metal  wire  having  an  un- 
magnetized  steel  knitting-needle  in  its  axis.  The  wire  coil  must  have 
an  insulating  coating,  in  order  to  keep  the  spark  from  breaking  across 
from  one  turn  to  the  next,  and  it  is  better  to  surround  the  steel  with 
a  glass  tube  to  prevent  the  possibility  of  the  sparks  passing  to  it. 

If  the  +  charge  of  a  jar  is  led  around  the  steel  in  the  direction 
shown  in  Fig  350,  the  left-hand  end  of  the  steel  will  become  a  north 
pole  and  the  right-hand  end  a  south  pole.    The  steel  has  become  a. 
magnet. 


466 


ELECTRICITY. 


If  you  stand  facing  the  end  which  has  become  a  south  pole,  you 
will  notice  that  the  +  charge  has  passed  around  the  steel  in  the  same 
direction  as  the  hands  of  a  clock  revolve.  This  rule  is  always  true. 

These  experiments  will  succeed  best  if  the  conductor  wrapping 
around  the  outer  coating  of  the  jar  is  a  wet  string,  which  offers  great 
resistance  to  the 
passage  of  the 
spark.  When  the 
circuit  is  all  com- 
posed of  good 
conductors  like 
copper  wire,  the 
discharge  of  the 
jar  is  oscillatory. 
The  electrifica- 
tions of  the  coat- 
ings reverse  thou- 
sands of  times 
during  the  short 
interval  of  the 
discharge.  Each 
reversal  involves 
a  partial  reversal 
of  the  polarity  of 
the  steel  wire,  and 
at  each  reversal 
the  poles  become  FlG  350.— MAGNETIZING  EFFECT  OF  SPARK  ON  STEEL  BAR. 
feebler  until  the 

oscillation  dies  away.  The  two  cases  of  discharge  are  like  a  deflected 
pendulum  swinging  in  a  viscid  liquid  and  in  air.  In  the  liquid,  the 
pendulum  will  fall  to  its  position  of  repose  without  oscillation ;  in 
air,  it  comes  to  rest  after  many  oscillations  of  diminishing  amplitude. 
Should  the  experiment  be  repeated  with  the  steel  bar  reversed  in 
position,  the  polarity  of  the  steel  will  be  reversed.  The  north  pole 
will  still  be  to  the  left.  If,  however,  the  +  charge  is  led  around  the 
coil  in  the  opposite  direction,  the  north  pole  will  be  to  the  right  hand, 
in  accordance  with  the  rule  before  given. 

Another  Magnetic  Action  of  the  Discharge. — Sup- 
pose the  two  terminals  of  the  Holtz  machine  to  be  connected 
by  means  of  binding  screws  with  a  wire  wound  in  a  coil 
around  a  suspended  magnetic  needle,  consisting  of  several 


THE  GALVANOMETER. 


467 


FIG.  351.— PRINCIPLE  OF  THE  MIRROR 
GALVANOMETER. 


bits  of  watch-spring  pasted  on  the  back  of  a  small  mirror. 

Let  the  mirror  hang  on  a  silk  fiber  attached  to  a  support  on 

the   coil.      The  position  of 

the  mirror  is  determined  by 

the  little   magnets  upon  it, 

as  they  set  in 

a    north     and 

south  direction 

like  a  compass- 
needle.  A  beam  of  light  is 

thrown  upon  the  mirror  and 

reflected  upon  a  scale,  A. 

Any  motion  of  the  mirror  is 

revealed  by  the  motion  of 

the  spot  of  light  upon  the 

scale.  This  device  is  shown  in  diagram,  Fig.  351,  where 
the  coil  is  greatly  enlarged  ^  while 
the  real  instrument  is  represented  in 
Fig.  352.  Such  an  instrument  is 
called  a  Galvanometer. 


The  coil  is  composed  of  a  large  number 
of  windings,  and  is  covered  with  a  brass  case 
for  protection.  The  mirror-needle  is  made 
sensitive  by  a  larger  magnet  (n  s,  Fig.  352), 
which  also  points  north  and  south,  but  has 
its  poles  so  placed  that  it  tends  to  turn  the 
suspended  needles  about,  end  for  end.  When 
the  large  magnet  is  slipped  down  upon  its 
supporting  rod  until  the  suspended  needle 
is  almost  on  the  point  of  reversing  its  posi- 
tion, the  latter  is  then  extremely  sensitive  to 
the  action  of  any  other  magnet. 

If  the  Holtz  machine  is  now  turned,  the 
positive  electricity  pours  from  the  +  knob 
through  the  wire  of  the  galvanometer  to  the 
—  knob.  The  mirror-needle  is  deflected  and 
the  watch-spring  magnets  all  tend  to  turn 
east  and  west,  or  into  a  longitudinal  position 


FIG.  352.— THE  MIRROR 
GALVANOMETER. 


468  ELECTRICITY. 

within  the  coil.  This  action  is  opposed  by  the  unbalanced  part  of  the 
attraction  of  the  earth,  which  tends  to  keep  the  mirror-magnets  in  a 
north  and  south  direction.  The  mirror  comes  to  rest  in  an  interme- 
diate position,  when  these  two  forces  balance. 

If  the  effect  of  the  earth  on  the  needle  were  to  be  wholly  balanced 
by  the  reverse  effect  of  the  bar  n  s  of  Fig.  352,  the  effect  of  the  dis- 
charge through  the  coil  would  be  to  turn  the  mirror-magnets  exactly 
into  a  longitudinal  position. 

In  such  experiments  the  Leyden-jars  should  all  be  removed  from 
the  Holtz  machine  in  order  to  avoid  the  danger  of  the  destruction  of 
the  insulation  in  the  coil  by  a  spark. 

The  Electric  Current.  —  When  the  wheel  of  the 
Holtz  machine  is  turned  while  the  knobs  are  connected 
with  the  galvanometer,  as  in  the  previous  experiment,  a 
continuous  discharge  pours  through  the  wire,  producing  a 
constant  deflection  of  the  needle.  As  soon  as  the  machine 
is  stopped,  the  discharge  ceases.  Such  a  flow  of  electricity 
along  a  wire  is  called  an  Electric  Current. 

The  current  is  maintained  by  means  of  the  work  applied 
to  the  crank  of  the  machine,  in  the  same  way  that  a  current 
of  water  can  be  maintained  in  a  pipe  circuit  by  means  of 
work  applied  to  operate  a  pump. 

Other  properties  of  an  electrical  current  will  be  explained 
more  fully  after  means  for  producing  stronger  currents  have 
been  treated.  The  voltaic  battery,  described  in  the  follow- 
ing chapter,  is  simply  a  machine  which  by  chemical  action 
gives  rise  to  a  continuous  electric  current. 

QUESTIONS.— Describe  a  battery  of  Leyden-jars.  How  are  their  outer  coatings 
placed  in  communication  ?  How,  their  knobs  ?  Why  is  such  a  combination 
called  a  battery  ?  On  account  of  its  powerful  effects.  May  the  discharge  be 
dangerous  ?  Relate  an  experience  of  Prof.  Van  Musschenbroek.  On  what  does 
the  effect  of  the  electrical  spark  depend  ?  How  are  bad  conductors  affected  ? 
Describe  experiments  in  which  the  spark  may  be  made  to  puncture  a  book  ;  a 
piece  of  glass.  WTiat  are  Geissler  tubes  ?  Describe  the  discharge  in  rarefied 
gases.  Will  the  spark  traverse  a  vacuum  ? 

Explain  the  discharge  in  air  and  the  analogy  between  it  and  the  discharge  in  the 
Geissler  tube.  State  the  condition  of  air-particles  along  the  line  of  the  dis- 
charge. When  does  Lightning  occur  ?  Describe  lightning-flashes  as  illustrated 
by  instantaneous  photographs.  How  may  you  calculate  their  distance  from 
you  ?  For  what  is  the  lightning-rod  intended  ?  How  are  disasters  averted 
through  its  agency  ?  What  should  be  the  height  of  the  rod  ?  How  much  space 


VOLTAIC  ELECTRICITY.  469 

does  it  protect  ?  To  what  depth  should  it  extend  into  the  ground,  and  why  ? 
Is  it  necessary  to  point  lightning-rods  ?  Account  for  the  duration  of  thunder  ; 
the  sudden  crash  after  a  moment  of  silence.  What  is  the  duration  of  a  light- 
ning-flash ?  Prove  your  answer.  What  places  are  most  dangerous  during  a 
thunder-storm  ?  Why  is  it  safe  to  be  in  bed  ?  Explain  the  Aurora. 
Describe  the  magnetizing  effect  of  the  spark  on  a  steel  needle.  Explain  the  Mir- 
ror Galvanometer  ;  the  action  of  the  curved  magnet ;  the  effect  of  the  passage 
of  electricity  through  the  coil  of  wire.  Define  an  Electric  Current.  Can  you 
give  a  reason  for  the  purity  of  the  air  after  an  electric  storm  ?  (Suggestion : 
Ozone  possesses  remarkable  chemical  activity  ;  it  is  a  powerful  corroder  and 
deodorizer.) 

EXPERIMENTS  IN  FRICTIONAL  ELECTRICITY. — The  pupil  may  construct  the  ap- 
paratus necessary  for  the  following  experiments  :  ELECTRIC  BELLS. — Suspend  two 
toy  bells  from  a  frame,  and  hang  a  brass  button  between  them.  Connect  one  of 
the  bells  with  the  conductor  of  a  machine,  and  the  other  with  the  ground.  When 
the  machine  is  in  action,  the  button  is  attracted  to  the  first  bell,  strikes  it,  becomes 
itself  charged  by  the  contact,  and  is  repelled  till  it  strikes  the  second  bell.  Its 
positive  electricity  is  thus  discharged,  and  it  falls  back,  to  be  again  attracted  and 
repelled.  DANCING  IMAGES.— On  a  metallic  plate  supported  by  some  conducting 
substance,  place  several  light  figures  cut  out  of  pith,  paper,  or  cork,  and  three 
or  four  inches  above  them  suspend  another  plate  from  the  conductor.  As  soon 
as  the  machine  is  worked,  the  figures  will  dance  up  and  down  from  one  plate  to 
another  in  a  laughable  manner.  Explain  the  principle.  THE  ELECTRIC  Kiss. — 
Attempt  to  kiss  a  person  on  an  insulating  stool,  while  he  holds  a  chain  con- 
nected with  the  conductor  of  an  electrical  machine  in  action.  DIVERGING 
THREADS.— Tie  together  at  each  end  a  cut  skein  of  twenty  linen  threads,  about 
ten  inches  in  length.  Attach  them  to  a  conductor,  and  when  the  machine  is 
operated  they  will  assume  an  oval  form.  Why  ?  ELECTRIFIED  HAIR.— Fix  a 
heavy  copper  wire  to  a  doirs  head  furnished  with  hair,  and  insert  the  wire  in  one 
of  the  holes  in  the  conductor  of  your  machine.  When  the  plate  is  turned,  the 
hairs  will  stand  grotesquely  on  end.  Draw  off  the  electricity  by  presenting  your 
knife-blade,  and  they  at  once  fall.  MULTIPLICATION  OP  THE  ELECTRIC  SP^TRK.— 
When  the  continuity  of  a  conductor  is  broken,  sparks  dart  from  one  part  of  it  to 
another.  Paste  pieces  of  tin-foil  about  one  eighth  inch  apart  on  a  length  of  glass 
tube,  furnish  the  tube  with  tin  caps,  and  place  one  cap  in  communication  with 
the  conductor  and  the  other  with  the  ground.  As  the  sparks  pass,  the  pattern  is 
rendered  luminous.  A  glass  globe  may  be  substituted  for  the  tube. 


VOLTAIC  ELECTRICITY.— CELLS  AND  BATTERIES. 

The  Voltaic  Cell. — If  a  piece  of  zinc  be  dipped  in 
dilute  sulphuric  acid,  the  zinc  will  be  attacked  by  the  acid 
and  replace  hydrogen  in  it.  The  zinc  and  hydrogen  sul- 
phate become  hydrogen  and  zinc  sulphate.  The  hydrogen 
appears  in  bubbles  on  the  zinc,  and  passes  off  as  a  gas.  At 
the  same  time,  for  each  gramme  of  zinc  consumed,  a  definite 
amount  of  heat  is  evolved ;  the  liquid  becomes  warm. 


470 


ELECTRICITY. 


If  a  piece  of  heavy  sheet-zinc  be  placed  in  dilute  sulphuric  acid 
(about  one  part  sulphuric  acid  to  nine  or  ten  of  water)  and  connected 

by  means  of  a  wire,  M,  with  a 
strip  of  copper,  C,  dipped  in 
the  same  solution,  the  zinc  will 
still  be  found  to  dissolve ;  but 
the  hydrogen  bubbles  will  now 
form  on  the  surface  of  the 
copper  strip  as  well  as  on  the 
zinc.  If  a  little  mercury  be 
rubbed  over  the  zinc,  no  gas 
will  now  form  thereon;  but 
when  the  copper  and  zinc 
plates  are  metallically  connect- 
ed, either  by  a  wire,  as  in  Fig. 
353,  or  by  touching  them  to- 

FIG.  353.— VOLTAIC  CELL.  gether    above    or    below    the 

liquid,  the  hydrogen   gas  all 

appears  on  the  surface  of  the  copper.  After  the  zinc  has  been  amal- 
gamated with  the  mercury,  it  is  best  not  to  touch  the  copper  plate  to 
it,  as  the  copper  will  also  amalgamate. 

Properties  of  the  Voltaic  Cell. — The  wire  which  con- 
nects the  copper  and  zinc  plates  of  the  voltaic  cell  has  many 
interesting  properties  so  long  as  it  is  in  contact  with  them. 
When  examined  with  delicate  instruments,  it  will  be  found 
to  be  heated.  It  will  magnetize  iron,  and  will  deflect  a 
magnetic  needle.  In  short,  its  properties  show  that  a  con- 
tinuous discharge  of  electricity  is  pouring  through  it,  the 
+  discharge  being  from  the  copper  to  the  zinc.  This  may 
be  proved  by  replacing  the  wire  M  with  the  wire  of  the  gal- 
vanometer coil ;  the  deflection  of  the  needle  shows  that  a 
current  is  passing  through  the  coil,  and  by  reversing  the 
connections  the  needle  is  deflected  in  the  opposite  direction. 

The  discovery  that  the  source  of  electricity  in  such  a  case  is  the 
contact  of  unlike  substances  was  made  about  1800  by  Alessandro  Volta, 
Professor  of  Physics  at  Pavia  (pah-ve'ah),  and  from  him  electricity 
produced  in  this  way  is  called  Volta'ic*  although  identical  with  that 


*  The  earliest  discovery  made  in  connection  with  this  kind  of  electricity  was 
that  of  Galvani  (gal-vah'ne),  Professor  of  Anatomy  at  Bologna,  that  the  contact 


THE  VOLTAIC   CELL. 

obtained  from  electrical  machines.  Volta's  celebrated  Pile  consisted 
of  a  series  of  pairs  of  copper  and  zinc  plates,  separated  from  one  another 
by  pieces  of  wet  cloth.  The  whole  was  insulated,  and  a  wire  attached 
to  each  end.  When  the  wires  were  brought  together  or  separated,  a 
spark  was  produced,  and  a  person  taking  one  of  the  wires  in  each  hand 
received  a  shock. 

The  effects  of  Voltaic  electricity  may  be  familiarly  illustratedc 
Place  a  piece  of  zinc  under  the  tongue,  and  on  the  tongue  a  silver  coin. 
As  long  as  the  metals  do  not  touch,  nothing  is  perceived ;  but  as  soon 
as  they  are  brought  in  contact,  the  Voltaic  circuit  is  formed,  a  thrilling 
sensation  is  felt  in  the  tongue,  and  a  taste  like  copperas  is  perceptible ; 
if  the  eyes  are  closed,  a  faint  flash  of  light  is  seen.  Here  electricity 
is  developed  by  the  chemical  action  of  saliva  upon  the  zinc. 

Lay  a  silver  dollar  on  a  sheet  of  zinc,  and  on  the  coin  place  a  liv- 
ing snail  or  angle- worm.  No  sooner  does  the  creature,  in  moving  about, 
get  partly  off  the  dollar  and  on  the  zinc,  than  it  receives  a  shock  and 
recoils.  In  this  case,  it  is  the  slime  of  the  snail  or  worm  that  acts 
chemically  on  the  zinc. 

Materials  used  in  a  Voltaic  Cell. — The  plates  of  the 
voltaic  cell  may  be  made  of  any  two  metals  which  are  un- 
equally acted  upon  by  the  liquid  in  which  they  dip,  the 
object  being  to  produce  a  difference  of  potential.  The 
liquid  may  be  either  pure  or  acidulated  water,  or  salt  solu- 
tions of  various  kinds. 

The  choice  of  materials  is  determined  by  the  use  which 
is  to  be  made  of  the  cells,  the  trouble  of  keeping  the  cell  in 
order,  and  the  presence  or  absence  of  offensive  fumes  which 
may  result  from  the  chemical  action  in  the  cell. 

In  all  forms  of  battery  in  practical  use,  zinc  serves  as 
the  plate  which  is  to  be  most  acted  upon.  The  other  plate 
is  usually  of  copper,  platinum,  or  carbon,  and  is  not  acted 
upon  at  all. 


of  metals  produces  muscular  contraction  in  the  hind-legs  of  a  frog  (1790).  Gal- 
vani's  experiment  is  often  repeated  at  the  present  day.  Separate  the  legs  of  a 
frog  from  the  body,  skin  them,  lay  a  thin  curved  zinc  rod  under  the  nerves  of  the 
loin,  and  touch  the  muscles  of  one  leg  with  a  similar  rod  of  copper.  The  instant 
the  rods  are  brought  in  contact,  the  leg  will  be  convulsed.  Galvani  believed  these 
movements  to  be  caused  by  the  passage  of  electricity  from  the  nerves  to  the  mufi- 
cles,  through  the  metal  rods  whicn  served  as  conductors. 


ELECTRICITY. 

A  battery  may  be  made  of  two  zinc  plates,  one  of  which  has  been 
cast  and  the  other  hard  rolled.  Even  a  difference  of  temperature  be- 
tween two  plates,  otherwise  precisely  alike,  will  give  a  feeble  electrical 
current.  When  the  two  plates  are  exactly  alike,  whether  they  are 
acted  upon  by  the  liquid  or  not,  no  current  will  result. 

Local  Action  upon  the  Battery-Plate. — Neighbor- 
ing points  upon  a  plate  of  commercial  zinc  are  always  suffi- 
ciently unlike  to  produce  a  current  between  them.  One 
point  in  the  plate  may  be  harder  than  another  near  by,  or 
it  may  be  under  a  different  pressure  by  reason  of  internal 
stresses  developed  in  solidification ;  or  impurities  may  exist 
in  different  degrees  at  the  two  points.  All  these  condi- 
tions will  result  in  setting  up  local  currents  upon  the  plate, 
which  is  thus  dissolved  without  producing  electrical  action 
through  the  connecting  wire. 

When  mercury  is  rubbed  over  the  plate,  it  dissolves  the  zinc,  oblit- 
erating the  effects  of  internal  stresses,  but  does  not  dissolve  such  im- 
purities as  carbon  or  iron  which  float  out  into  the  liquid.  A  clean, 
homogeneous  surface  of  zinc  is  thus  exposed  to  the  liquid.  The  zinc 
does  not  dissolve  in  the  acid  except  when  the  plates  of  the  cell  are  con- 
nected by  the  wire  w,  or  some  conductor  other  than  the  liquid  in  which 
both  are  dipped.  The  current  then  pours  through  the  connecting  wire. 

Polarization  of  the  Battery-Plate. — After  the  bat- 
tery has  been  in  action  for  a  short  time,  the  copper  plate 
becomes  covered  with  a  film  of  hydrogen.  The  cell  is  then 
said  to  be  polarized.  While  the  plate  is  in  this  condition, 
the  current  is  much  feebler  than  when  it  is  clean.  This  is 
shown  by  means  of  the  galvanometer.  The  deflection  of  the 
needle  diminishes  as  the  current  becomes  feebler.  The  hy- 
drogen can  be  brushed  off  the  plate  by  mechanical  means, 
or  may  be  removed  by  lifting  the  plate  into  the  air.  These 
methods  are  not  very  effective,  as  the  hydrogen  immediately 
reappears  on  the  plate.  The  most  effective  way  of  removing 
it  is  by  immersing  the  copper  plate  in  some  liquid  which 
will  combine  chemically  with  the  hydrogen  as  it  appears. 
The  cells  next  to  be  described  are  designed  for  this  purpose. 


VARIETIES   OF  CELLS, 

The  Gravity  Cell. — In  this  cell,  the  copper  is  placed  in 
a  solution  of  copper  sulphate  (blue  vitriol)  in  the  lower  part 
of  the  vessel.  The  zinc  is  suspended  _= — -  - — _ 

in  the  upper  part  of  the  cell,  in  a  jrflT     ^f°\ 

solution  of  zinc  sulphate.     The  cop-  3t-3 

per  sulphate  solution  has  a  higher 
specific  gravity  than  the  zinc  sul- 
phate, and  this  keeps  the  two  liquids 
separate.  An  insulated  wire,  having 
an  exposed  end  fastened  to  the  cop- 
per by  a  rivet,  passes  out  of  the  top 

*  J  *        FIG.  354.— GRAVITY  CELL. 

of  the  cell  and  forms  the  +  wire  of 

the  cell.     The  negative  wire  is  usually  clamped  in  a  bind- 
ing screw  attached  to  the  zinc  above  the  liquid. 

When  the  hydrogen  appears  on  the  copper  plate,,  surrounded  by 
the  copper  sulphate  solution,  it  replaces  the  copper  of  the  copper  sul- 
phate. Instead  of  hydrogen  and  copper  sulphate,  we  have  copper, 
which  is  deposited  on  the  copper  plate,  and  hydrogen  sulphate  (sul- 
phuric acid).  As  a  result,  therefore,  copper  instead  of  hydrogen  is  de- 
posited on  the  copper  plate.  The  sulphuric  acid  diffuses  through  the 
liquid  and  attacks  the  zinc,  forming  zinc  sulphate.  The  zinc  is  thus 
continually  dissolved.  The  copper  sulphate  is  also  consumed,  and  is 
replaced  by  dropping  in  a  few  crystals  of  the  substance  whenever  the 
blue  color  in  the  lower  solution  has  nearly  disappeared.  The  lighter 
zinc  sulphate  solution  must  occasionally  be  siphoned  off  with  a  rubber 
tube,  and  water  should  be  poured  in  carefully. 

In  a  dry  room,  evaporation  at  the  top  of  the  liquid  causes  crystals 
of  zinc  sulphate  to  form  on  the  jar  just  above  the  liquid.  The  liquid 
rises  through  these  crystals  by  capillary  action,  and  crystals  form  higher 
up.  Thus  the  salt  moistened  with  liquid  will  finally  creep  over  the  top 
of  the  jar  and  down  upon  the  shelf  and  floor.  This  is  prevented  by 
brushing  a  little  raw  linseed-oil  upon  the  glass  above  the  liquid. 

Various  forms  of  the  gravity  cell  are  used  by  thousands 
in  telegraphing.  Both  the  zinc  and  copper  plates  are  made 
in  various  patterns.  In  the  older  Daniell  cell,  the  two  liquids 
were  separated  by  a  porous  jar  of  earthenware. 

In  the  Grove  Cell,  nitric  acid  is  used  in  place  of  the 
copper  sulphate  solution,  and  for  the  same  purpose. 
31 


4:74. 


ELECTRICITY. 


FIG.  355.— THE  GROVE 
CELL. 


As  copper  is  rapidly  acted  upon  by  nitric  acid,  Grove 
substituted  platinum.  In  Fig.  355,  P  is  the  platinum  sheet, 
placed  in  a  porous  jar  containing  the 
acid.  The  zinc  is  bent  in  a  U-form 
around  the  porous  jar.  The  whole  is 
placed  in  a  jar  of  glazed  earthenware, 
here  shown  broken  away  to  reveal  the 
interior  parts.  The  outer  jar  contains 
dilute  sulphuric  acid  in  contact  with  the 
zinc. 

The  Bunsen  Cell  differs  from  that 
of  Grove  only  by  the  substitution  of  a 
stick  of  carbon,  made  from  gas  coke, 
for  the  platinum  sheet.  This  cell,  when 
worked  through  short,  heavy  wires,  gives 
better  results  than  the  gravity  cell ;  but  the  liquids  must 
be  replaced  after  a  few  hours  of  action,  and  this  occasions 
trouble  and  expense.  The  Bunsen  cell  also  gives  off  corro- 
sive fumes,  due  to  the  decompo- 
sition of  the  nitric  acid  by  the 
hydrogen  (see  page  471). 

A  solution  of  4  parts  of  sodium 
bichromate,  4  of  sulphuric  acid,  and 
18  of  water,  may  replace  the  nitric 
acid  in  the  Bunsen  cell.  This  solution 
gives  off  no  fumes.  The  bichromate 
salt  is  dissolved  in  water,  and  the  sul- 
phuric acid  slowly  added,  while  the 
liquid  is  stirred.* 

The     Leclanche     Cell     is 

shown  in  Fig.  356.     The  zinc  is 
usually   in  the   form  of    a  rod, 


FIG.  356.— LECLANCHE  CELL. 


*  Water  should  never  be  poured  into  sulphuric  acid  ;  the  heat  developed  is 
great  enough  to  vaporize  the  water  explosively,  and  serious  accidents  may  occur. 
The  acid  must  be  poured  slowly  into  the  water  ;  stir,  as  you  pour,  with  a  glass 
rod. 


DIP-BATTERIES. 


4T5 


which  stands  in  one  corner  of  the  outer  vessel.  The  porous 
jar  contains  the  carbon  plate  packed  in  fragments  of  coke 
and  powdered  manganese  dioxide,  which  acts  in  oxidizing 
the  hydrogen-bubbles.  The  liquid  is  a  solution  of  ammo- 
nium chloride  in  water. 

This  cell,  having  small  power,  is  much  used  in  working  house- 
bells,  telephones,  railway-signals,  etc.,  where  it  is  required  only  occa- 
sionally and  for  a  short  time.  It  will  not  stand  continuous  work  like 
the  gravity  cell,  as  the  manganese  oxide  acts  slowly  and  the  cell  polar- 
izes, requiring  time  to  recover.  The  advantage  of  the  Leclanche  cell 
is,  that  it  may  be  closed  up  in  a  box  to  prevent  evaporation  and  left  for 
a  year  without  attention. 

Dip-Batteries. — Various  forms  of  cells  have  been  con- 
structed, which  allow  the  zinc  plates  to  be  lifted  from  the 
solution  when  not  in  actual  use. 

In  the  bichromate -of  potash  cell,  shown  in  Fig.  357,  usu- 
ally made  in  bottle-form,  the  zinc  is  carried  on  a  rod  held 


FIG.  357. — BICHROMATE 
BOTTLE  CELL. 


FIG.  358.— DIP  CELLS  USED  WITH  THE  EDISON 
ELECTRIC  PEN. 


by  gentle  friction  in  a  sleeve  at  the  top  of  the  cell.     By 
pulling  upward  upon  the  rod,  the  zinc  may  bs  raised. 

In  Fig.  358  all  the  plates  of  two  cells  are  attached  to  a 
cross-piece  which  slides  upon  a  vertical  rod  between  the 
cells.  The  rod  is  mounted  upon  a  bed-plate  of  iron,  upon 
which  the  cells  also  rest.  The  plates  are  held  in  position 


476  ELECTRICITY. 

when  out  of  the  solutions  by  means  of  a  gravity  latch-piece, 
which  drops  into  a  notch  in  the  vertical  rod.  One  liquid 
only,  the  bichromate  of  potash  solution,  is  used.  It  yields 
no  noxious  fumes,  and  is  in  that  regard  preferable  to  nitric 
acid.  Hence  these  cells  are  much  used  for  table-work. 

Arrangement  of  Cells  in  a  Battery. — When  the 
wires  leading  to  a  galvanometer  are  attached  to  the  zinc 
and  carbon  plates  of  a  battery  cell,  instead  of  to  the  knobs 
of  the  electric  machine,  as  in  Fig.  351,  the  mirror-needle  is 
permanently  deflected.  This  shows  that  a  current  of  elec- 
tricity is  flowing  in  the  wire.  The  stronger  the  current,  the 
greater  the  angle  of  deflection  of  the  needle. 

If  it  is  desired  to  get  a  stronger  current  than  is  given  by 
one  cell,  a  number  of  cells  may  be  connected  so  as  to  act 
together.  In  Fig.  359  four  cells  are  joined,  the  zinc  of  each 
being  connected  with  the  carbon  or  copper  of  the  next. 

The  current  from  each  cell  then  flows  through  all  the 
others.     Cells  thus  arranged   are  said  to  be 
in  series. 

G 


FIG.  359. — ARRANGEMENT  OF  CELLS  TO  FORM  A  BATTERY — IN  SERIES. 

In  Fig.  360,  the  four  cells  have  their  zincs  all  connected 
by  a  metal  conductor,  the  coppers  or  carbons  being  similarly 
connected.  These  main  conductors  are  then  connected  by 
wires  with  the  galvanometer.  Such  cells  are  said  to  be 
connected  in  multiple  or  in  parallel  circuit. 


ARRANGEMENT  OF  CELLS  IN  BATTERIES.   47? 


When  the  cells  are  in  multiple,  the  current  from  any  one  cell  does 
not  flow  through  any  other  cell,  but  the  separate  currents  are  forced 
out  in  parallel  streams  through  the  conducting  wires  and 
galvanometer. 


FIG.  360.— ARRANGEMENT  OF  CELLS  TO  FORM  A  BATTERY— IN  PARALLEL  CIRCUIT. 

The  Proper  Arrangement  of  the  Cells  of  a  battery 
depends  entirely  upon  the  kind  of  battery  used,  and  the 
nature  of  the  external  circuit. 

If  it  is  desired  to  send  a  current  through  a  long,  thin 
wire,  and  one  cell  gives  an  insufficient  current,  other  cells 
must  be  added  in  series,  as  in  Fig.  359.  The  longer  and 
smaller  the  wire,  the  greater  the  number  of  cells  required. 
If  a  coil  of  wire,  r  (Fig.  359),  be  connected  in  the  circuit, 
the  current  will  become  feebler.  More  cells  mast  be  added 
in  series  in  order  to  force  the  same  current  as  before  through 
the  circuit. 

If  the  circuit  is  made  up  of  large  copper  wires,  connected 
with  a  galvanometer  consisting  of  one  turn  of  large  wire, 
then,  if  one  cell  gives  an  insufficient  effect,  the  added  cells 
should  be  in  multiple.  The  current  is  not  materially  in- 
creased by  adding  cells  in  series  with  the  short,  large  con- 
ductors of  Fig.  360,  nor  by  adding  them  in  multiple  with 
the  long  fine  wires  of  Fig.  359.  It  appears  that  the  conduct- 
ing wires  offer  a  resistance  to  the  passage  of  the  electricity  ; 
that  this  resistance  increases  with  the  length  of  the  conduct- 
or, and  diminishes  as  the  size  of  the  wire  increases. 

The  battery  acts  in  a  twofold  way.  It  drives  the  current  through 
the  wire  and  also  serves  as  a  conductor,  since  the  current  must  flow 
through  the  battery.  If  the  battery-plates  are  small,  the  effect  is  to 


4T8 


ELECTRICITY. 


make  the  resistance  great,  as  is  the  case  with  a  wire  when  its  section 
is  small.  In  Fig.  360,  if  only  one  cell  is  acting,  its  resistance  is  large 
as  compared  with  that  of  the  wire  conductors.  If  the  three  other  cells 
be  added  in  multiple,  they  will  act  precisely  as  one  cell  of  four  times 
the  section.  The  effect  is  to  diminish  the  battery  resistance  to  one 
fourth  of  that  of  one  cell,  the  battery  resistance  comprising  nearly  the 
whole  resistance.  The  power  of  the  four  cells  for  driving  electricity 
through  the  wire  when  thus  connected  is  the  same  as  for  one  cell,  as 
will  be  shown  later  (page  480). 

In  Fig.  359  the  resistance  of  one  cell  is  small  compared  with  that 
of  the  long,  fine  wire.  When  the  three  cells  are  added  in  line,  the  bat- 
tery resistance  is  made  four  times  as  great,  since  it  amounts  to  an  in- 
crease in  the  length  of  the  conductor  ;  but  the  battery  resistance  is 
still  insignificant  as  compared  with  that  of  the  wire.  The  resistance 
of  the  whole  circuit  has  not,  therefore,  been  materially  changed  ;  but 
the  power  of  the  battery  to  drive  electricity  through  resistance  is 
four  times  as  great.  Hence  an  increase  of  the  current  results. 

Analogy  between  the  Action  of  Pumps  and  Bat- 
teries. —  Suppose  it  is  desired  to  force  a  gallon  of  water  a 

second  through  a  long, 
narrow  pipe  (R,  Fig. 
361).  A  pump  of  large 
section  operated  by  a 
man  is  found  to  drive 
only  about  a  quarter  of 
the  required  amount. 
Four  such  pumps  may 
then  be  connected  in 
series,  so  that  the  wa- 
ter passes  through 
them  all,  as  shown  in 
the  figure.  If  the  pis- 
tons are  worked  in 
unison,  the  driving 
force  is  four  times  as 
great  as  when  only 


FIG.  361.— ILLUSTRATING  PUMPS  IN  SERIES. 


one  pump  is  worked,  and  the  amount  of  water  discharged 
a  second  will  be  very  nearly  four  times  as  great. 


PUMP  AND  BATTERIES  COMPARED. 


4T9 


If,  however,  water  is  to  be  forced  through  a  very  large 
tube,  K,  as  in  Fig.  362,  little  will  be  gained  by  adding 
pumps  in  series,  should  one  pump  like  those  represented 
be  insufficient.  The  water  -  current  is  throttled  in  the 
pump  instead  of  in  the 
conducting  -  pipe.  The 
discharge  may  be  increased 
by  adding  pumps  in  par- 
allel, as  in  Fig.  362.  The 


1 

g 

?r 

• 

& 

l_ 

^ 

'-. 

P1 

W 

1 

I 

1 

£ 

f 

f- 

FIG.  362.— ILLUSTRATING  PUMPS  IN  PARALLEL  CIRCUIT. 

pressure  which  drives  the  water  is  not  thereby  increased. 
The  pumps  balance  one  another.  The  four  pumps  simply 
act  as  one  pump  of  greater  section,  but  with  no  greater 
pressure  per  square  inch. 


480  ELECTRICITY. 

Similarly,  in  an  electric  battery,  if  the  current  is  throttled  by  high 
resistance  in  the  conducting  wire  which  it  is  not  feasible  to  diminish, 
cells  must  be  added  in  series  to  increase  the  electro-motive  force  suffi- 
ciently to  drive  the  desired  current  through  the  resistance. 

If  the  current  is  throttled  in  the  battery,  its  resistance  may  be 
diminished  by  increasing  the  sectional  area  of  the  battery  liquid 
through  which  it  must  flow.  This  is  done  by  connecting  cells  in 
parallel,  and  an  increase  in  the  strength  of  the  current  will  result. 

QUESTIONS.— Define  an  Electric  Current.  An  electric  current  is  a  continuous 
transference  of  electricity  between  bodies  having  a  difference  of  potential. 
Apply  this  principle  in  a  description  of  a  Voltaic  cell.  How  can  you  prove  that 
the  current  flows  from  the  copper  to  the  zinc  ?  Why  is  electricity  produced  in 
this  way  called  Voltaic  ?  Describe  Galvani's  experiments,  and  state  his  theory. 
Give  Volta's  correction  of  this  theory.  Describe  the  Voltaic  pile.  Suggest  some 
familiar  illustrations  of  Voltaic  electricity. 

Enumerate  the  materials  used  in  the  Voltaic  cell.  Prove  that  the  source  of  Vol- 
taic electricity  is  chemical  decomposition.  What  is  the  cause  of  local  currents, 
and  how  do  they  affect  the  action  of  a  cell  ?  State  the  effect  of  rubbing  mer- 
cury on  the  zinc  plate.  What  is  meant  by  polarization  of  the  plate  ?  How  is  it 
corrected  ?  Explain,  with  the  aid  of  sketches,  the  gravity,  Grove,  Bunsen,  Le- 
clanche,  and  bichromate  cells.  Why  is  the  latter  preferred  for  table-work  ? 
Describe  the  arrangement  of  cells  in  a  battery  in  series  ;  in  multiple  or  paral- 
lel. On  what  does  the  proper  arrangement  of  the  cells  depend  ?  Explain  your 
answer.  In  what  two  ways  does  a  battery  act  ?  Compare  with  the  action  of 
pumps  differently  arranged. 

If  a  charged  battery  is  to  be  kept  for  some  time  ready  for  use,  why  is  it  impor- 
tant to  take  care  that  the  ends  of  the  wires  are  not  connected  outside  the  bat- 
tery ?  To  detect  the  presence  of  a  bullet  or  piece  of  metal  in  the  tissues,  a 
probe  is  used  consisting  of  two  pieces  of  insulated  wire  attached  to  small  plates 
of  zinc  and  copper.  The  copper  is  placed  on  one  side  of  the  tongue,  the  zinc 
on  the  other,  and  the  wound  is  probed.  State  how  the  surgeon  will  be  made 
aware  of  the  presence  of  the  metallic  body  when  the  tips  of  the  wires  touch  it. 
Explain  the  principle.  Sum  up  the  differences  you  have  observed  between 
the  current  from  a  Voltaic  battery  and  that  from  a  Holtz  machine,  as  regards 
intensity,  ease  of  production,  heating  and  magnetic  effects,  power  of  chemical 
decomposition,  and  impression  on  the  nervous  system. 


ELECTRICAL  RESISTANCE.— THE  OHM. 

Unit  of  Electrical  Resistance.  —  When  electricity 
flows  through  any  medium  or  circuit,  it  meets  with  resist- 
ance. We  can  always  determine  how  much  greater  is  the 
resistance  offered  by  any  piece  of  wire  than  that  offered  by 
some  standard  of  resistance. 

The  unit  of  resistance,  called  the  Ohm  (ome),  is  the  re- 


RESISTANCE  COILS. 


481 


sistance  of  a  column  of  pure  mercury  having  a  section  of 
one  square  millimetre  and  a  length  of  106-28  centimetres  at 
a  temperature  of  0°  C.  A  copper  wire  having  the  same  sec- 
tion and  resistance  must  have  a  length  of  6,090  centimetres, 
and  a  German-silver  wire,  a  length  of  485-4  centimetres. 

Conductors  of  the  same  size  and  having  twice  these  lengths,  will 
have  a  resistance  of  two  ohms.  Thus  the  resistance  is  proportional  to 
the  lengths.  If  wires  twice  as  thick  are  used,  the  resistance  is  one  half 
as  great.  Thus,  a  copper  wire,  hav- 
ing a  length  of  twenty  feet  and  a 
section  of  two  square  millimetres, 
will  have  the  same  resistance  as  a 
wire  of  the  same  material  ten  feet 
in  length  and  one  square  milli- 
metre in  section. 

Resistance  Coils. — Coils 
of  wire  having  known  resist- 
ances can  be  purchased  of 
instrument-makers.  They  are 
arranged  as  shown  in  Fig.  363. 
The  wire  is  wound  upon  a  spool,  like  thread,  and  is  doubled 
upon  itself  at  the  middle,  the  two  halves  being  wound  side 
by  side.  The  coils  do  not  then  become  magnets  when  a  cur- 
rent passes  through  them. 

The  spools  are  fastened  on  the  under  side  of  the  cover 

of  a  box  in  which  many 
such  spools  are  mounted. 
The  ends  of  the  wires  con- 
nect with  other  wires 
which  pass  up  through 
the  cover,  and  are  soldered 

FIG.  364.-SET  OF  CONNECTED  BARS,  RESIST-    to  heawbraSS  bai^C'C'C3. 

ANCE-BOX.  J 

These  bars  can  be  con- 
nected with  one  another  by  means  of  metallic  plugs,  P,  P 
(Fig.  363),  thus  forming  a  continuous  conductor. 

If  the  wires  of  a  battery  are  connected  with  the  extremities  D  E 
(Fig.  364)  of  such  a  set  of  connected  bars,  all  having  coils  beneath,  the 


FIG.  363.— RESISTANCE  COILS. 


482 


ELECTRICITY. 


current  will  flow  through  the  bars  and  plugs,  which  offer  only  an  in- 
significant resistance  by  reason  of  their  large  size.  If  any  plug  is 
pulled  out,  the  current  must  then  flow  through  the  coil  of  wire  be- 
neath, whose  resistance  is  thus  added  to  the  circuit. 

Coils  in  a  Resistance-Box. — The  coils  of  an  ordinary 
resistance-box  are  as  follows  : 

1  2  2  5  10  10  20  50 

5000      2000      1000      1000        500          200          100          100 

The  coil  marked  1  is  composed  of  a  wire  whose  resist- 
ance is  one  ohm.  The  two-ohm  coil,  if  made  of  wire  of  the 

same  size,  must  be 
twice  as  long,  etc. 
The  higher  resist- 
ances, like  1,000 
ohms,  are  usually 
made  of  very  much 
smaller  wire  than 
that  comprising 
the  smaller  resist- 
ances ;  the  coils 
would  otherwise 
become  too  large. 
By  properly  choos- 
ing the  sizes  of  the  wire,  the  coils  can  all  be  made  of  about 
the  same  size. 

A  set  of  coils  lifted  out  of  the  box  is  shown  in  Fig.  365.  A  box 
like  the  one  described  above  will  measure  any  resistance  between  1  and 
10,000  ohms. 

Standard  Resistances. — Let  a  standard  coil  be  placed 
in  a  water-tight  metal  box,  and  the  ends  of  the  wire  con- 
nected with  large  copper  conductors  (W,  W,  Fig.  366), 
which  when  in  use  dip  into  small  dishes  of  mercury,  serving 
as  connections.  As  the  resistance  of  all  substances  varies 
with  temperature,  these  coils  are  standard  at  some  definite 
temperature.  When  in  use,  the  coil  is  immersed  in  water, 
the  temperature  of  which  is  measured  by  a  thermometer. 


FIG.  365.— INTEKIOR  OF  Box  OF  COILS. 


MEASUREMENT  OF  RESISTANCE. 


483 


The  corrections  for  temperature  are  similar  to  those  which  must 
be  applied  to  a  metre-bar  in  order  to  allow  for  expansion. 

The  increase  in  resistance  for  each  ohm  when  heated  through  1° 
C.  is  for  copper  wire  0*0038  ohm  ;  and  for  Ger- 
man silver  (composed  of  copper  4  parts,  nickel 
2  parts,  zinc  1  part)  the  coefficient  per  ohm- 
degree  C.  is  0-00044.  Thus  100  ohms  of  cop- 
per at  0°  C.  become  100  +  100x25x0-0038  = 
109-50  ohms  at  25°  C. 

The  Measurement  of 
Resistances.  —  To  meas- 
ure the  resistance  of  a  tele- 
graph line,  the  distant  end 
is  connected  with  the 
ground,  as  at  G'  (Fig.  367), 
by  means  of  a  gas  or  water 
pipe  system.  In  the  ab- 
sence of  these,  a  gas-pipe 
may  be  driven  down  to 
moist  earth,  and  water  may 
be  poured  into  the  hole 
around  the  pipe.  A  well  into  which  an  iron  rod  dips  may 
also  be  used.  One  plate  of  the  battery,  B,  is  also  grounded 
at  G.  The  other  plate  is  connected  with  the  line  at  D 
through  a  delicate  galvanometer,  V,  and  the  resistance-box, 
R,  the  plugs  being  all  in  place. 

The  galvanometer-needle  is  deflected  and  its  position  is  noted. 
The  line  is  then  disconnected  at  D,  and  the  battery  wire  at  C  is  dis- 
connected and  attached  to  D.  Resistances  are  then  introduced  by 
pulling  plugs  from  the  box  until  the  needle  is  again  at  the  same  posi- 
tion. The  coils  within  the  box  form  an  artificial  line,  and  their  resist- 
ance is  equal  to  that  of  the  actual  line.  In  the  first  measurement, 
the  earth  is  excluded,  but  it  is  so  large  that  its  resistance  is  insignifi- 
cant if  good  connections  are  made  at  the  earth  plates,  Gr  and  G'. 

This  is  learned  by  measuring  two  grounded  wires  upon  the  same 
poles  between  any  two  stations,  as  New  York  and  Washington.  The 
distant  ends  are  then  disconnected  from  the  ground  and  connected 
with  each  other.  The  near  ends  are  also  disconnected  from  the  ground 


FIG.  366.— STANDARD  COIL  IMMERSED  IN 
WATER. 


484: 


ELECTRICITY. 


and  connected  with  binding  screws  at  C  and  D.  The  two  wires  then 
form  a  loop  from  the  testing-table  in  New  York  to  Washington  and 
back.  The  resistance  of  the  two  lines  in  this  measurement  is  found 


FIG.  367.— MEASUREMENT  OF  RESISTANCE. 

to  be  the  same  as  the  sum  of  the  resistances  of  the  lines  when  grounded. 
This  shows  that  the  earth  between  New  York  and  Washington  has 
practically  no  resistance. 

In  the  loop  measurement,  the  two  wires  are  connected 
into  the  circuit  exactly  as  the  wire  coil,  W,  would  be  if  its 
extremities  were  connected  at  C  and  D,  and  the  ground  and 
line  were  disconnected  at  those  points.  The  resistance  of 
the  coil  W  can  evidently  be  found  in  the  same  way. 


MEASUREMENT  OF  RESISTANCE. 


485 


The  resistance  of  No.  9  iron  telegraph  wires  is  about  16 
ohms  to  the  mile. 

This  way  of  ascertaining  unknown  resistance  in  terms  of  standard 
coils  is  like  one  method  of  finding  the  weight  of  a  body ;  see  page  84. 

Measurement  of  Resistance  by  means  of  the  Dif- 
ferential Galvanometer. — The  differential  galvanometer 
consists  of  two  coils,  W,  of  insulated  copper  wire  (Fig.  368). 

The  coils  should  have  the  same  number  of  windings,  and 
should  be  as  near  alike  in  all  respects  as  possible.  They  are 


FIG.  368.— PRINCIPLE  OF  THE  DIFFERENTIAL  GALVANOMETER. 

mounted  on  the  ends  of  two  rods  which  slide  with  gentle 
friction  through  the  sides  of  a  box.  The  ends  of  the  wire 
forming  the  coils  terminate  in  four  binding  screws  upon  the 
side  of  the  box.  Between  the  coils,  suspended  on  a  fiber  of 
silk,  is  a  small  magnetized  needle  or  other  suitable  magnet. 
A  wire  from  either  end  of  a  battery  communicates  at  A 
with  two  branches,  one  of  which  connects  with  S  through 
the  plugged  resistance-box,  the  other  with  S3.  The  current 
is  then  led  through  the  galvanometer  coils  to  the  screws  S8 


486  ELECTRICITY. 

and  S4,  from  which  wires  uniting  at  B  return  the  current 
to  the  other  end  of  the  battery.  At  any  point  in  the  bat- 
tery line  between  A  and  B,  a  key,  K,  is  fixed,  by  depressing 
which  the  circuit  is  closed. 

The  two  coils  of  the  galvanometer  are  so  placed  and  connected 
that  they  tend  to  deflect  the  needle  90°.  but  in  opposite  directions 
when  the  key  is  closed.  If  the  two  branches  have  equal  resistances, 
each  will  carry  half  of  the  battery  current.  They  may  be  so  adjusted 
by  sliding  one  of  the  connecting  wires  through  the  binding  screw,  as 
at  S3.  The  position  of  the  coils  is  adjusted  by  sliding  them  in  or  out 
on  the  rods.  The  adjustment  is  complete  when  opening  and  closing 
the  key  produces  no  deflection  of  the  needle. 

The  needle  is  made  more  sensitive  by  means  of  two  bar-magnets, 
N  S,  lying  on  the  table  parallel  to  it.  If  it  sometimes  points  wrongly, 
the  magnets  N  S  may  by  patient  adjustment  be  made  to  restore  it  to  its 
proper  position.  The  sensitiveness  of  the  needle  will  also  be  increased 
by  placing  the  coils  nearer  together. 

Now  connect  the  coil  r,  whose  resistance  is  to  be  measured,  with 
the  branch  not  containing  the  resistance-box.  The  resistance  of  this 
coil  obstructs  the  current  in  that  branch,  and  more  than  half  now 
flows  through  the  other  branch,  the  galvanometer  coil  of  which  has  a 
greater  effect  than  the  one  in  the  branch  of  greater  resistance.  If 
plugs  are  now  pulled  from  the  resistance-box  until  on  opening  and 
closing  the  key  the  needle  is  again  in  balance,  the  added  resistance  in 
the  box  is  equal  to  that  of  the  coil  V. 

This  operation  precisely  resembles  the  determination  of 
weights  by  a  lever-balance  of  equal  arms,  where  the  un- 
known weight  is  counterpoised  by  standard  weights. 

Faults  on  Telegraph  Lines  and  Cables. — When  an 
overland  line  breaks,  its  resistance  becomes  practically  in- 
finite. The  break  is  usually  located  without  difficulty  by 
simple  inspection,  so  that  electrical  methods  are  unneces- 
sary. In  ocean  cables  it  is  important  to  locate  the  break  in 
order  that  the  cable  may  be  grappled  and  raised  as  near  as 
possible  to  the  fault. 

The  resistance  of  a  given  cable  in  a  perfect  condition  is  known, 
being  frequently  measured.  When  the  cable  breaks,  it  makes  a 
"  ground  "  in  the  water.  If  this  ground  is  one  third  of  the  way  across 


FAULTS.  487 

from  the  American  to  the  foreign  terminus,  the  resistance  from  the 
American  side  at  once  drops  to  one  third  of  that  determined  by  previ- 
ous measurements,  provided  the  foreign  ground  connection  is  broken. 
In  a  similar  way  the  fault  can  be  located  by  measurements  from  the 
foreign  end,  which  will  show  a  resistance  of  two  thirds  of  the  whole 
cable  resistance. 

Sometimes  the  fault  is  not  complete,  but  involves  merely 
leakage  through  a  crack  in  the  insulation.  The  fault  itself 
will  then  have  an  appreciable  resistance,  and  the  measure- 
ment from  the  American  end  will  locate  the  break  too  far 
away  from  our  shore.  Measurement  from  the  foreign  end 
will  then  locate  it  too  far  from  the  foreign  shore,  the  fault- 
resistance  being  in  each  case  measured  with  the  fraction  of 
cable.  The  sum  of  the  two  will  be  greater  than  the  resist- 
ance of  the  perfect  cable.  The  break  then  lies  midway  be- 
tween the  two  points  thus  located. 

Caution  in  measuring  Resistance. — In  all  cases 
where  the  resistance  of  a  coil,  as  W  in  Fig.  368,  is  to  be 
measured,  the  coil  must  be  far  enough  from  the  galvanom- 
eter not  to  deflect  the  needle  directly.  Such  a  coil  when 
traversed  by  a  current  becomes  an  electro-magnet.  It  is  to 
avoid  such  trouble  that  the  wires  of  resistance-coils  are 
doubled  on  themselves,  as  was  previously  explained. 

QUESTIONS.— Explain  Electrical  Resistance.  What  is  the  Unit  of  Resistance 
called  ?  Compare  the  resistance  of  a  column  of  mercury  with  that  of  a  copper 
and  of  a  German-silver  wire  of  the  same  length  and  section.  State  the  relation 
between  resistance  and  length  of  wire  ;  between  resistance  and  thickness  of 
wire.  What  are  resistance-coils  ?  How  are  they  connected  with  batteries  ? 
Describe  a  resistance-box.  What  is  the  effect  of  temperature  on  the  resist- 
ance of  substances  ?  How  are  standard  resistance-coils  applied  in  measuring 
the  resistance  of  telegraph  lines  ?  Compare  the  mode  of  ascertaining  unknown 
resistance  in  terms  of  standard  coils  with  a  method  of  finding  the  weight  of  a 
body  by  the  use  of  the  spring-balance. 

Describe  the  Differential  Galvanometer,  and  explain  its  use  in  the  measurement 
of  resistance.  Compare  its  operation  with  the  determination  of  weight  by  a 
lever  balance.  What  effect  on  its  resistance  has  a  break  in  an  overland  line  ? 
How  are  breaks  in  cables  and  underground  wires  located  ?  Explain  what 
occurs  when  the  fault  involves  leakage  merely.  How  is  the  place  of  leakage 
found  ?  Why  are  the  wires  of  resistance-coils  doubled  on  themselves  ? 


4:88  ELECTRICITY. 


MEASUREMENT  OF  CURRENTS.— THE  AMPERE. 

The  Unit  of  Current  is  called  the  Ampere  (am-pare1). 
If  a  current  is  passed  through  a  solution  of  copper  sulphate 
(blue  vitriol)  by  means  of  two  copper  plates  having  the  form 
shown  in  Fig.  353,  copper  will  be  deposited  on  one  plate 
and  dissolved  from  the  other.  The  plate  connected  with 
the  zinc  plate  of  the  battery  will  receive  a  deposit  of  cop- 
per. The  other  plate  will,  if  of  pure  copper,  lose  an  equal 
amount.  As  it  usually  contains  impurities  which  are  in 
part  washed  off  into  the  liquid,  the  loss  of  this  plate  is  gen- 
erally a  little  greater  than  the  gain  of  the  other. 

An  ampere  will  deposit  0-327  milligramme  of  copper  a 
second,  or  1-177  grammes  an  hour. 

A  current  of  how  many  amperes  will  therefore  deposit 
one  kilogramme  an  hour  ?  A  current  of  how  many  amperes 
will  deposit  one  pound  an  hour? 

The  amount  of  silver,  copper,  and  gold  deposited  per  hour  by  one 
ampere  is  given  in  the  table  below  :— 


SUBSTANCE. 

Grammes  per 
Ampere  per  hour. 

SUBSTANCE. 

Grammes  per 
Ampere  per  hour. 

Hydrogen  ... 

0-03738 

Gold          ... 

S'44480 

Silver  .  . 

4-02500 

1'18330 

If  the  current  is  passed  through  water,  the  water  is  also  decom- 
posed into  its  constituent  gases,  hydrogen  and  oxygen.  The  hydrogen 
is  liberated  at  the  plate  connected  with  the  zinc  plate  of  the  battery, 
while  oxygen  forms  at  the  other.  These  gases  may  be  collected  in 
tubes  in  the  usual  manner,  and  the  amounts  of  gas  are  found  by  meas- 
uring the  volumes  (Fig.  369).  The  water  must  be  slightly  acidified  in 
order  to  make  it  a  good  conductor. 

The  plates  used  for  the  decomposition  of  substances  are 
called  electrodes.  The  one  attached  to  the  zinc  wire  is 
called  the  negative  electrode,  or  cathode,  and  the  other  is 
the  anode.  Hydrogen  and  metallic  substances  are  deposited 


DECOMPOSITION  OF  WATER. 


489 


on  the  cathode.  In  decomposing  water,  both  electrodes  are 
of  platinum,  in  order  that  the  gases  set  free  may  not  act 
chemically  upon  them. 

Relation   of  Electrodes   and   Battery-Plates. — In 

the  battery,  it  was  found  that  hydrogen  forms  on  the  plate 

toward  which 
the  current  is 
flowing  in  the 
cell.  The  cop- 
per or  carbon 
plate  is  sur- 
rounded by  an 
oxidizingliquid, 
in  order  to  re- 
move the  hydro- 
gen as  it  is  lib- 
erated. The 
acid  is  placed 
in  contact  with 
the  zinc.  In 
the  decompos- 
ing cell,  V  (Fig. 
370),  the  same 
thing  is  observed.  Hydrogen  and  all  metals  appear  on  the 
plate  toward  which  the  current  is  flowing  in  the  decompos- 
ing cell. 


FIG.  369.— DECOMPOSITION  OP  WATER. 


If  a  solution  of  cop- 
per sulphate  is  placed  in 
V,  the  copper  is  deposit- 
ed on  the  plate  marked 
a,  while  the  other  plate 
will  have  around  it  an 
accumulation  of  sulphu- 
ric acid.  In  the  gravity  battery,  copper  deposits  on  the  plate  C,  while 
the  sulphuric  acid  is  liberated  around  the  zinc  plate  Z. 

If  V  is  a  large  plating- vat,  it  is  found  that  the  electrodes  act  like 
a  battery,  but  tend  to  send  a  current  in  the  opposite  direction  from 
32 


FIG.  370.— ACTION  OP  ELECTRODES. 


490  ELECTRICITY. 

that  of  the  battery.  If  the  battery  is  taken  out  of  the  circuit,  this 
current  is  easily  shown  by  the  deflection  of  a  galvanometer-needle. 
The  current  from  the  electrodes  is  always  feebler  than  that  from  the 
battery,  and  when  the  two  are  connected  the  result  is  the  enfeeblement 
of  the  battery  current  by  the  decomposing  cell.  The  current  from 
the  electrodes,  due  to  the  chemical  action,  resists  the  battery  cur- 
rent, which  has  brought  about  the  chemical  action.  The  polarization 
of  the  battery-plates  themselves  is  an  action  of  the  same  kind. 

Measurement  of  Current  by  Magnetic  Action. — If 

a  wire  which  carries  a  current  from  several  Grove  cells  is 

passed  up  through  a  small  hole 
in  a  horizontal  plate  of  glass 
or  card  board,  and  iron-filings 
are  sprinkled  upon  the  glass 
from  a  sifter,  the  filings  will 


§§&^f  \  arrange  themselves  into  lines 
like  those  produced  by  a  mag- 
net. The  lines,  however,  are 
circular  in  form,  having  the 
wire  as  a  center. 

A  magnetized  sewing-nee- 
dle balanced  on  a  silk  fiber  or 
FIG.  STL-ARRANGEMENT  OP  IRON-     a  fine  hair  will  tend  to  set  tan- 

FILINGS  ON  A  PLATE  OP  GLASS.  , ,  , .  mi        -, . 

gent  to  these  lines.  The  di- 
rection of  its  north  pole  will  be  reversed  when  the  current 
is  reversed. 

If  a  piece  of  steel  had  only  a  north  pole  and  were  acted  upon  only 
by  the  current,  the  pole  would  revolve  round  the  wire  in  any  one  of 
the  circles  in  which  it  might  be  placed  when  the  current  was  started. 
A  south  pole  would  turn  in  the  opposite  direction.  As  every  piece  of 
steel  has  both  poles,  which  are  urged  in  opposite  directions,  the  needle 
sets  in  the  line  of  force. 

In  Fig.  371,  the  current  passes  upward  through  the  wire, 
and  the  arrows  on  the  plate  indicate  the  direction  in  which 
the  north  pole  points.  This  direction  may  be  remembered 
by  means  of 


AMPERE'S  RULE. 


491 


FIG.  372.— LINES  OF  FORCE  WHEN  THE  WIRE 
is  BENT. 


Ampere's  Rule. — Imagine  yourself  floating  in  the  cur- 
rent within  the  wire,  with  your  head  in  the  direction  in 
which  the  current  flows  and  facing  the  needle.  The  north 
pole  of  the  needle  will  always  be  on  the  left  hand.  A  piece 
of  soft  iron  lying  in  this  position  would  be  magnetized, 
with  the  polarity  which 
would  produce  equilib- 
rium according  to 
Ampere's  rule.  This 
magnetic  action  of  a 
current  is  utilized  in  all 
galvanometers. 

If  the  wire  is  bent  into 
a  circular  form,  as  in  Fig. 
372,  the  lines  of  force  re- 
vealed by  iron-filings  upon 
a  glass  plate  are  no  longer 

concentric  circles.  Along  the  axis  of  the  wire  a  c  a',  the  line  of  force  is 
a  straight  line.  A  north  pole  placed  on  the  right  at  a  would  move  to  c, 
then  to  a',  and  then  on  to  an  infinite  distance  to  the  left  along  this  line, 
if  acted  upon  only  by  the  current.  All  the  other  lines  are  closed  curves 
encircling  the  wire.  The  arrows  show  the  position  of  a  magnet-needle. 

In  a  galvanometer,  the  needle  is  hung  at  C.  The  coil  is 
turned  so  that  the  needle,  N  S,  is  in  the  plane  of  the  coil. 
When  the  current  is  turned  on,  the  needle  sets  at  such  an  an- 
gle that  the  forces  of  the  earth  and  coil  balance  each  other. 

The  Ampere-Meter. — Currents  are  measured  by  means 
of  an  Ampere-meter,  of  which  one  form  is  illustrated  in 
Fig.  375.  A  short,  lozenge-shaped  needle,  n  s,  is  mounted 
on  a  small  shaft,  P,  as  shown  in  section  (Fig.  373).  The 
needle  and  shaft  turn  on  a  jeweled  pivot,  and  are  mounted 
between  the  poles  of  two  strong  curved  magnets,  M,  which 
give  direction  to  the  needle,  n  s.  The  current  is  passed 
around  two  coils,  C.  of  large  wire,  the  size  of  which  depends 
on  the  magnitude  of  the  currents  to  be  measured. 

If  the  current  in  the  coil  should  alone  act  on  the  needle,. 


4:92 


ELECTRICITY. 


the  latter  would  turn  90°  from  the  position  shown  in  Fig, 
373.  If  the  current  increases  from  zero,  the  needle  will 

turn  through  a  greater 
and  greater  angle.  The 
motion  of  the  needle  is 
revealed  by  a  pointer,  I 
(Fig.  374),  which  moves 
over  a  scale  graduated 
to  amperes  (Fig.  375). 

This  scale  is  graduated 
as  follows:  Any  temporary 
scale  of  equal  divisions  is 
placed  under  the  index,  I. 
The  instrument  is  connect- 
ed in  circuit  with  a  battery 
and  a  copper  decomposing 
cell,  the  copper  electrodes 
having  first  been  weighed. 
As  the  battery  may  become 
weak,  the  current  is  kept 
constant  by  moving  the 
plates  nearer  together,  and 
thus  diminishing  the  resistance.  The  plates  should,  therefore,  clamp 
on  a  rod,  so  as  to  allow  readily  of  such  motion.  The  reading  of  the 
index,  I,  is  thus  to 
be  kept  constant. 

If  in  30  minutes 
it  is  found  that  5-9 16 
grammes  of  copper 
have  been  deposit- 
ed, this  would  be  at 
the  rate  of  11-833 
grammes  per  hour. 
As  one  ampere  de- 
posits 1-1833  per 
hour,  the  current 

must  have  been  10  amperes.  On  the  permanent  scale,  reading  in  am- 
peres, this  point  should  therefore  be  marked  10.  Increase  or  diminish 
the  current  by  changing  the  number  of  cells  or  by  varying  the  resist- 
ance, and  other  points  of  the  scale  may  be  similarly  determined. 


Fio.  373.— PLAN  OF  AMPERE-METER. 


FIG.  374. 


FIG.  375.— AMPERE-METER. 


THE  VOLT.  493 

The  Tangent  Galvanometer,  which  may  also  be  used 
to  measure  strong  currents,  consists  of  a  coil  of  wire  whose 
plane  is  vertical,  and  coincides  with  the  plane  of  the  mag- 
netic meridian.  At  the  center  of  the  coil  is  a  short  mag- 
netic needle,  with  a  pointer  attached,  which  plays  around 
the  graduated  circle  of  a  compass-box. 

When  no  current  is  passing,  the  needle  points  to  magnetic  north 
and  south.  But,  when  a  current  is  sent  through  the  coil,  it  tends  to 
deflect  the  needle  at  right  angles  to  the  coil.  The  strength  of  the  cur- 
rent to  a  certain  extent  determines  the  amount  of  this  deflection,  which 
is  always  proportionate  to  the  tangent  of  the  angle  of  deflection.  If 
the  coil  be  turned  90°,  so  that  the  needle  stands  at  right  angles  to  it, 
and  the  current  is  then  sent  around  in  the  proper  direction,  it  will  not 
affect  the  needle,  which  is  already  where  the  current  tends  to  place  it. 

QUESTIONS.— What  do  you  mean  by  the  Ampere  ?  How  much  copper  will  one 
ampere  deposit  in  a  second  ?  How  much  silver  in  an  hour  ?  Explain  how 
water  may  be  decomposed  by  a  current.  What  are  electrodes  ?  Distinguish 
by  name  positive  and  negative  electrodes.  Describe  the  relation  between  elec- 
trodes and  battery-plates.  Which  current  is  feebler— that  from  electrodes  or 
that  from  the  battery  ?  When  the  two  are  connected,  what  is  the  result  ? 

How  does  the  deflection  of  a  magnetic  needle  furnish  a  ready  method  of  detecting 
when  and  in  what  direction  a  current  flows  ?  State  Ampere's  rule  for  aiding 
the  memory.  Illustrate  the  application  of  this  rule  by  holding  the  wire  in 
various  positions,  above,  below,  parallel  to  the  needle,  etc.  How  do  iron-filings 
arrange  themselves  on  a  glass  plate  through  which  passes  a  current-carrying 
wire  ?  How,  when  the  wire  is  bent  into  a  circular  form  ?  Describe  in  detail 
the  Ampere-Meter  ;  the  Tangent  Galvanometer. 


ELECTRO-MOTIVE  FORCE.— THE   VOLT. 

By  the  Electro-motive  Force  of  a  Battery  or  cell, 
is  meant  its  power  of  driving  electricity  through  the  re- 
sistance of  the  circuit.  It  is  sometimes  called  electrical 
pressure.  The  unit  electro-motive  force,  or  difference  of 
potential,  is  called  the  Volt.  It  is  the  electrical  pressure 
required  to  maintain  a  current  of  an  ampere  through  a  re- 
sistance of  an  ohm. 

The  relation  of  current,  resistance,  and  potential  difference,  can  be 
illustrated  by  a  current  of  water.  In  Fig.  376,  T  represents  a  tank  of 
water,  in  which  the  water  is  maintained  at  a  fixed  level  by  means  of  a 


494 


ELECTRICITY. 


pump,  while  the  tank  discharges  through  a  pipe  B  o.  At  regular  in- 
tervals glass  tubes,  serving  as  manometers  (see  page  198),  are  tapped 
into  the  discharge-tube.  The  height  to  which  the  water  rises  in  each 
tube  indicates  the  pressure.  At  the  mouth  of  the  main  tube,  the  press- 
ure is  zero;  it 
rises  uniformly 
toward  the  tank. 
The  current 
of  water,  in 
quarts  per  sec- 
ond, is  the  same 
in  all  parts  of  the 


FIG.  376.— ANALOGY  BETWEEN  ELECTRICAL 
PRESSURE  AND  WATER  PRESSURE  ILLUS- 
TRATED. 


tube.  The  press- 
ure of  the  col- 
umn of  water, 
B  e,  is  required 

to  force  the  current  through  the  resistance  of  the  pipe  C  o. 
The  pressure  of  the  column  P  h  is  required  to  force  the 
same  current  through  the  resistance  P  o.  If  P  o  is  three  times  as 
great  as  C  o,  then  P  h  must  be  three  times  as  great  as  C  0.  From  B 
to  o  the  resistance  is  represented  to  be  seven  times  as  great  as  from 
C  to  o,  and  the  pressure  of  B  e  is  also  seven  times  as  great  as  C  o. 

The  fall  of  pressure  is  the  same  through  each  unit  of  resistance. 
From  A  to  P  it  is  the  difference  between  columns  H  and  h.  This  dif- 
ference in  pressure  is  what  is  required  to  maintain  the  current  through 
the  resistance  of  A  P,  and  it  is  the  same  as  C  0,  or  one  seventh  of  B  e. 
If  the  pipe  were  half  the  section,  the  same  pressure  B  e  would  de- 
liver only  half  the  current.  The  pressure  line  e  H  h  o  would,  however, 
remain  the  same.  If  the  discharge-pipe,  on  the  other  hand,  were  twice 
as  long,  the  effect  would  also  be  to  reduce  the  current  to  one  half. 
Both  of  these  changes  would  double  the  resistance  of  the  discharge- 
pipe.  To  get  the  same  current  as  before,  the  water  in  the  tank  would 
have  to  be  raised  to  twice  the  height  B  e.  The  fall  of  pressure  for 
each  unit  of  resistance  is  thus  seen  to  be  always  the  same  for  the  same 
current.  All  these  statements  are  true  for  a  current  of  electricity. 

Electrometers  arc  used  for  measuring  potential  or 
electric  pressure.  One  form  of  the  quadrant  electrometer  is 
shown  in  Fig.  377.  Four  insulated  hollow  quadrants  of 
brass  have  suspended  within  them  a  flat  hour-glass-shaped 
needle  of  aluminum.  In  Fig.  378  the  quadrants  are  shown 


THE  QUADRANT  ELECTROMETER. 


495 


as  seen  from  above,  and  with  the  upper  plates  broken  away 

to  reveal  the  needle.      Quadrants  diagonally  opposite  are 

connected  by  wires.      The 

needle    hangs    on    a    silk 

fiber,  and  connects  below, 

by  means   of  a    platinum 

wire,  with  sulphuric  acid, 

which    forms     the    inner 

coating  of  a  Leyden-jar,  L, 

Fig.  377.      The  acid  and 

needle    are    electrified   by 

means  of  the    Holtz  ma- 
chine, and  in  the  best  forms 

of  electrometer   there   are 

devices  for  detecting  and 

restoring  leakage,  so  as  to 

maintain  a  fixed  charge  on 

the  jar  and  needle. 

If   the   insulations   are 

all  clean  and  dry,  the  leakage  will  be  very  small.    The  needle 

sometimes  has  a  small  magnet  attached  to  it,  which  gives  it 

direction.  It  must  be  placed 
symmetrically  with  respect  to 
the  quadrants,  as  indicated. 

rj_          When  the  wires 

of  a  battery  are  con- 
nected with  adjacent 
quadrants,  they  be- 
come    charged,     as 
shown  in  Fig.  378  ;  the  needle  is  re- 
pelled by  the  +  quadrants  and  at- 
tracted by  those  charged—.     The 
angle  of  deflection  is  read  by  abeam 
of  light  reflected  from  a  mirror. 

Adding  cells  in  line,  as  in  Fig. 
359,  increases  the  deflection.  It 
increases  the  charge  on  the  quadrants.  It  increases  their  electrical 
pressure  or  potential.  It  makes  the  +  quadrants  more  strongly  posi- 


FIG.  377.— THE  QUADRANT  ELECTROMETER. 


T 


FIG.  378.— PRINCIPLE  OF  QUADRANT 
ELECTROMETER. 


496 


ELECTRICITY. 


tire,  and  the  —  quadrants  more  strongly  negative.  If  the  space  sepa- 
rating the  quadrants  is  narrow,  the  pressure  difference  would  become 
so  great,  by  adding  thousands  of  cells,  that  the  charge  would  break 
through  the  insulation  of  air  between  the  quadrants,  a  spark  would 
pass,  and  the  battery  would  maintain  the  discharge.  We  should  prac- 
tically have  an  electric  light. 

Adding  cells  in  parallel,  as  in  Fig.  360,  does  not  change  the  po- 
tential. When  cells  are  arranged  in  parallel-series,  the  deflection  de- 
pends only  on  the  number  of  cells  in  each  line,  and  not  upon  the 
number  of  lines. 

In  Fig.  379,  the  line  represented  in  Fig.  367  is  shown  in 
diagram.  If  one  set  of  quadrants  of  the  electrometer  E  be 
grounded,  and  the  other  connected  with  the  line  at  A,  the 
needle  will  be  strongly  deflected.  If  the  contact  is  made 


GROUND  GROUND  GROUND 

FIG.  379.— QUADRANT  ELECTROMETER  IN  CONNECTION  WITH  TELEGRAPH  LINE. 

at  B,  the  deflection  will  be  less,  and,  as  the  contact  slides  to 
the  ground  at  C,  the  deflection  will  fall  to  zero.  Contact 
being  made  at  D,  the  deflection  will  be  in  the  opposite  direc- 
tion, but  it  will  again  fall  to  zero  at  F.  The  potential  falls 
along  the  line  A  C,  in  the  same  way  that  the  pressure  falls 
in  the  pipe  (Fig.  376). 

If  a  battery  of  1,500  Grove  cells  were  connected  in  the  line,  it 
would  be  fatal  for  one  to  stand  on  the  ground  and  touch  the  wire  at  A 
(Fig.  379).  The  human  body  would  offer  a  rather  high  resistance,  but 
the  potential  there  is  so  much  above  that  of  the  ground  that  a  fatal 
current  would  be  driven  through  the  body.  At  B  the  danger  would 
be  less,  and  it  would  diminish  to  nothing  at  C. 

Ohm's  Law. — The  relation  of  current,  resistance,  and 
potential,  is  expressed  by  Ohm's  law.* 


*  The  units  ohm,  ampere,  and  volt,  were  named  in  honor  of  the  three  great 
electricians— Ohm,  Ampere,  and  Volta. 


OHM'S  LAW.  49Y 

We  have  learned  that  one  volt  of  electric  pressure  will 
maintain  a  current  of  one  ampere  through  one  ohm  of  re- 
sistance. Two  volts  will  be  required  to  maintain  the  same 
current  through  two  ohms.  R  volts  will  drive  an  ampere 
through  R  ohms. 

If  we  double  the  current  through  R  ohms,  we  must  double  the 
pressure ;  hence — 

2  R  volts  will  drive  two  amperes  through  R  ohms.  Similarly,  for 
any  number  of  amperes,  C. 

C  R  volts  will  drive  C  amperes  through  R  ohms.  If  E  represents 
this  number  of  volts,  or  the  electro-motive  force,  then 

E  =  C  R,  or  C  =  ?. 
si 

This  equation  is  an  algebraic  statement  of  Ohm's  law. 
Expressed  in  words  it  is :  The  number  of  volts  required  to 
maintain  a  current  of  C  amperes  through  R  ohms  is  obtained 
by  multiplying  the  number  df  units  of  current  by  the  num- 
ber of  units  of  resistance. 

The  strength  of  the  current  C  is  directly  proportional  to 
the  electro-motive  force,  and  inversely  proportional  to  the 
resistance. 

If  any  two  of  the  quantities  in  the  equation  for  Ohm's 
law  are  found  by  measurement,  the  third  can  be  computed. 

Electro-motive  Force  of  Cells. — In  Fig.  376  the 
pressure  of  the  column  of  water  B  e  is  required  to  overcome 
the  resistance  of  the  pipe  B  o.  It  is  evident  that  the  pump 
itself  offers  resistance  to  the  passage  of  the  current,  and 
therefore  that  the  total  pressure  required  to  drive  the  cur- 
rent through  the  entire  circuit  is  really  greater  than  B  e. 

This  total  pressure  corresponds  to  the  electro-motive 
force  of  a  cell,  or  the  electric  pressure  required  to  drive  the 
current  through  the  battery  and  external  circuit.  Such 
electro-motive  force  depends  only  on  the  materials  used  in 
the  cell,  and  not  at  all  upon  its  size.  It  changes  somewhat 
as  the  liquids  are  exhausted  during  action. 


498  ELECTRICITY. 

The  electro-motive  force  in  the  case  of  different  cells  is 
as  follows  : 

Daniell  gravity    .       .       .       1  '07  volts     Bunsen  .....       1*94  volts 
Grove    .       .      .,  "*.';    '  .       1-93    "        LeclanchS    .       .-     ,       .       1'48    " 

If  196  Daniell  cells  were  connected  into  one  line,  the  electro- 
motive force  would  be  196  x  1-07  =  209-7  volts.  If  107  Grove  cells 
were  connected  in  line,  the  battery  would  have  an  electro-motive  force 
of  107  x  1-93  =  209-7.  If  these  batteries  were  connected  against  each 
other  in  one  circuit,  they  would  balance,  and  there  would  be  no  cur- 
rent in  that  circuit. 

In  the  same  way  it  can  be  shown  that  the  electro-motive  force  of 
a  battery  is  due  simply  to  the  cells  in  line.  If  100  cells,  all  in  parallel, 
be  connected  with  one  opposing  cell,  there  will  be  a  balance.  The  re- 
sistance of  the  battery  of  100  cells  will  be  the  one  hundredth  of  the 
resistance  of  one  cell  ;  but  their  electro-motive  forces  are  the  same. 
Similarly,  two  lines  of  25  cells  each,  in  parallel,  will  balance  one  line 
of  25  cells  when  connected  in  opposition  in  the  same  circuit.  In  the 
same  way  any  number  of  pumps,  working  in  parallel,  would  be  bal- 
anced by  a  single  pump  of  the  same,  kind  working  against  them  in  the 
discharge-pipe. 

Divided  Circuits.  —  When  a  battery-wire  divides  into 
two  branches,  as  in  Fig.  380,  the  current  also  divides  be- 
tween the  two  branches  as  a  current  of  water  would  divide 
in  a  branching  pipe.  The  sum  of  the 
two  currents  in  the  branches  will  be 
equal  to  the  current  in  the  undivided 
part.  The  fall  of  potential  from  a  to  b 
will  be  the  same  through  the  two  wires, 
as  the  fall  in  pressure  would  be  the 
same  in  the  two  branches  of  a  tube. 
The  pressure  in  the  branches  must  be 
FIG.  ^.-DIVIDED  BAT-  the  same  at  the  points  where  they 


The  currents  in  the  branches  are  inversely  as  their  resistances. 
The  current  will  be  least  in  the  branch  having  the  greatest  resistance. 
If  one  branch  be  broken,  its  resistance  will  become  infinite,  and  its 
current  will  be  zero.  If  one  resistance  be  practically  zero,  all  the  cur- 
rent will  flow  through  it. 


SHUNTED  GALVANOMETERS. 


499 


FIG.  881. 
LOOPED  WIRE. 


Fia.  382. 
DIVIDED  PIPE. 


If  the  wire  be  looped  (Fig.  381),  and  a  good  contact  be  made  at  c, 
no  current  will  flow  through  the  loop.  It  will  flow  directly  across  the 
joint  at  c.  In  a  divided  pipe 
(Fig.  882),  where  the  resist- 
ance of  one  branch,  A,  is 
very  small  compared  with 
that  of  the  other,  B,  the 
former  will  carry  all  the 
current.  In  B  there  will  be 
no  appreciable  flow. 

This  condition  is  real- 
ized in  a  resistance-coil  which  has  been  plugged  out  of  circuit.  The 
current  practically  all  flows  through  the  plug  instead  of  the  coil.  The 
resistance  of  the  plug  is  practically  zero.  When  the  plug  is  drawn,  the 
resistance  of  this  branch  becomes  infinite,  and  the  current  is  driven 
around  the  coil. 

The  same  result  would  follow  in  the  case  of  the  pipe,  if  the  short 
branch  A  were  closed.  The  current  would  all  flow  around  B,  whose 
resistance  would  be  introduced  into  the  circuit. 

Shunted  Galvanometers. — When  it  is  desirable  to 
measure  a  current  which  exceeds  the  capacity  of  a  galva- 
nometer, a  wire  may  be  connected  across  the  terminals  of 
the  galvanometer,  and  through  it  any  fraction  of  the  current 
may  be  deflected.  This  wire  is  called  a  shunt,  and  the  gal- 
vanometer is  said  to  be  shunted.  The  galvanometer  then 
measures  a  known  fraction  of  the  total  current. 

If  the  galvanometer  have  a  resistance  of  3-0  ohms  and 
the  shunt  a  resistance  of  \  of  3*0  or  0*33  ohm,  then  the  cur- 
rent in  the  galvanometer  will  be  -J-  of  the  current  in  the 
shunt,  or  ^  of  the  total  current. 

Similarly,  if  the  shunt  have  a  resistance  of  3*5-,  the  galvanometer 
resistance,  only  T^  of  the  total  current  will  be  measured. 

Shunt- wires  should  be  doubled  on  themselves,  like  other  resistance- 
coils,  so  that  they  do  not  become  electro- magnets. 


QUESTIONS. — Define  the  electro-motive  force  of  a  battery.  By  what  other  name 
is  it  sometimes  known  ?  Explain  its  relation  to  difference  of  potential.  What 
is  the  unit  electro-motive  force,  and  by  what  name  is  it  called  ?  By  what  anal- 
ogy may  the  relation  of  current,  resistance,  and  potential  difference,  be  illuS' 


500  ELECTRICITY. 

trated  ?  Draw  a  diagram  on  the  blackboard  to  demonstrate  that  the  fall  of 
pressure  for  each  unit  of  resistance  is  always  the  same  for  the  same  current. 

Explain  the  use  of  the  Quadrant  Electrometer  in  measuring  electric  pressure. 
Illustrate  the  instrument  by  diagram.  How  might  it  become  an  electric  light  ? 
Does  adding  cells  in  parallel  change  the  potential  ?  Under  what  circumstances 
would  it  be  dangerous  to  touch  the  wire  of  an  electric  circuit  ?  Why  ?  Re- 
peat Ohm's  law.  State  it  algebraically.  To  what  is  the  current  directly  pro- 
portional ?  To  what,  inversely  proportional  ? 

Compare  the  total  pressure  required  to  drive  a  current  of  water  through  a  pipe 
with  the  electro-motive  force  of  a  cell.  Oil  what  does  this  electro-motive  force 
wholly  depend  ?  Explain  the  balance  of  opposing  batteries  ;  of  100  cells  in 
parallel  and  one  opposing  cell ;  of  pumps  working  in  parallel  and  a  single  op- 
posing pump.  Describe  the  division  of  a  current ;  the  current  in  the  case  of  a 
looped  wire  ;  the  passage  of  water  through  a  divided  pipe.  What  is  meant  by 
a  shunted  galvanometer,  and  for  what  is  it  used  ? 


HEATING  EFFECTS  OF  CURRENTS. 

Heat  developed  by  Resistance. — A  short,  thin  wire 
of  platinum,  iron,  or  German  silver,  if  placed  in  the  circuit 
of  a  large  Bunsen,  Grove,  or  bichromate  cell,  will  become 
red-hot.  The  remaining  part  of  the  circuit  should  be  of 
short,  thick  wire.  This  is  a  case  of  the  development  of  heat 
at  a  point  of  high  resistance.  The  same  thing,  to  a  less  de- 
gree, would  happen  in  a  short,  narrow  section  of  tube,  in  a 
water-pipe  line  through  which  water  is  forced,  or  at  the 
door  of  a  crowded  audience-room  when  a  panic  occurs. 

The  short,  thin  wire  has  the  same  resistance  as  a  larger 
one  of  much  greater  length.  In  the  one  case,  the  heat  is 
generated  in  a  small  amount  of  material.  In  the  large  and 
long  wire  of  the  same  resistance,  the  same  heat  will  be  liber- 
ated in  a  much  greater  amount  of  metal,  and  the  rise  in 
temperature  will  accordingly  be  less.  The  temperature 
rises  until  the  heat  generated  in  the  wire  each  second  equals 
the  amount  radiated.  In  the  large  wire  the  radiating  sur- 
face per  ohm  of  resistance  is  much  greater  than  in  the 
other. 

Measurements  show  that  a  current  of  one  ampere  flowing  through 
an  ohm  of  resistance  will  yield  0-24  heat-unit  a  second;  that  is  to  say, 
each  ohm  of  the  wire  will  heat  0'24  gramme  of  water  through  1°  C.  in 


MEASUREMENT  OF  HEAT  OF  CURRENT. 


501 


one  second.    If  the  current  is  doubled,  the  heat  is  four  times  as  great, 
the  heat  liberated  being  proportional  to  the  square  of  the  current,  thus  : 

1  ampere  through  1  ohm  yields        0'24  heat-units. 

2  amperes      "       1    "        "      4  x  0'24         " 

3  "  "        1     "         "       9  x  0'24          " 

4  "        1    "         "     16  x  0  24 

The  amount  of  heat  in  two  ohms  will,  in  each  case,  be  twice  as 
great,  and  increases  directly  with  the  resistance. 

The  Calorimeter,  shown  in  Fig.  383,  is  used  for  meas- 
uring the  heat  developed  in  a  wire  carrying  a  current. 

The  wire,  K,  is  immersed  in  a  badly  conducting  liquid 
contained  in  the  vessel,  C.     Heavy 
refined  coal-oil  is  generally  used  ; 
alcohol  or  distilled  water,  however, 
will  answer  the  purpose. 

The  current  is  measured  by  a 
galvanometer,  and  the  difference 
in  potential  in  volts  on  the  two 
binding  screws  may  be  determined 
by  means  of  an  electrometer  con- 
nected with  them  as  before  ex- 
plained. The  resistance  can  then 
be  computed,  and  the  amount  of 
heat  which  should  be  liberated  per 
second  can  easily  be  found. 

The  rise  in  temperature  of  the 
liquid  is  measured  by  a  thermom- 
eter, T.  A  stirrer,  S,  is  used  to 
mix  the  liquid  so  as  to  secure  a 
uniform  temperature. 

The  calorimeter,  C,  is  supported  by 
its  flanged  lip,  which  rests  upon  a  felt 
washer,  C'.  When  in  use,  the  calorimeter  may  be  placed  in  a  tin  can, 
which  is  mounted  in  a  box  containing  loosely  packed  sawdust.  This 
is  intended  to  prevent  loss  of  heat  by  radiation. 

The  heat  generated  by  the  current  is  0*24  x  C2  x  R  x  t,  in  which  C 
is  the  current  in  amperes,  R  the  resistance  of  the  coiled  wire  within 


FIG.  383. — CALORIMETER  FOR 

MEASURING  HEAT  IN  CUR- 
RENT- CARRYING  WlRE. 


502  ELECTRICITY. 

the  liquid,  and  t  the  number  of  seconds  the  current  is  allowed  to 
pass. 

Problems.  —  The  heat  generated  is  also  found  from  the  rise  in  tem- 
perature of  the  liquid. 

Suppose  the  stirrer  and  can  to  be  of  brass,  to  heat  a  gramme  of 
which  one  degree  C.  requires  0*093  heat-unit.  If  they  weigh  200 
grammes,  then  for  each  degree  of  rise  shown  by  the  thermometer,  200  x 
0-093  =  18'6  heat-units  have  been  imparted  to  the  can. 

If  the  can  contains  w  grammes  of  water,  and  the  temperature  rise 
through  T  degrees  during  t  seconds,  the  heat  given  to  the  water  is  w 
T  heat-units.  The  whole  heat  generated  is  T  18'6  +  w  T  heat-units. 

These  two  quantities  of  heat  must  be  equal  to  each  other,  or  — 


If  the  calorimeter  contains  800  grammes  of  distilled  water  at  a 
temperature  10°  below  that  of  the  air,  and  is  heated  through  20°,  the 
heat  required  will  be 

20  x  18-6  +  800  x  20  =  16,372  units. 

If  the  resistance  of  the  wire  is  0-7  ohm  at  the  air  temperature,  and 
a  current  of  10  amperes  be  passed  through  it,  the  heat  liberated  each 
second  will  be 

0-24x100x0-7  =  16-8. 

The  current,  therefore,  must  run  974  seconds,  or  16  TO.  14  sec.,  to 
furnish  16,372  heat-units. 

Evidently  if  the  amount  of  water,  w,  the  rise  in  temperature,  T, 
the  current,  C,  the  resistance,  R,  and  the  time,  t,  be  all  observed,  the 
amount  of  heat  imparted  to  the  calorimeter  (here  18-6  T)  can  be  com- 
puted from  the  equation.  It  will  be  the  difference  between  the  heat 
generated  by  the  current  and  the  heat  given  to  the  water,  or  — 
0-24C9R*  -  wT. 

Heat-Waste  in  Wires.  —  In  all  wires  carrying  currents, 
a  part  of  the  electrical  power  is  wasted.  A  mile  of  pure 
copper  wire  having  a  diameter  of  0-23  inch  will  have  a  re- 
sistance of  one  ohm. 

The  heat  developed  per  second  in  such  a  wire  when  carrying  a 
current  of  ten  amperes,  as  is  done  in  arc-light  currents,  will  be 
0-24  x  100  x  1  =  24  heat-units. 

As  one  heat-unit  (gramme-degree)  is  equivalent  to  424-55  work- 
units  (gramme-meter)  (see  page  269),  this  heat  will  be  equivalent  to 


HEAT-WASTE   IN   WIRES.  503 

24x424-55  =  10,189  gramme- meters,  or  10-180  kilogramme-meters  per 
second.  As  one  horse-power  is  76  kilogramme-meters  per  second,  the 
power  lost  in  this  mile  of  wire  would  be 

10-180      A,0, 

— — —  =  0-13  horse-power. 

The  Watt. — Electrical  power  is  also  expressed  in  terms 
of  Watts,  one  Watt  being  the  power  of  a  current  of  one 
ampere  in  a  circuit  of  one  ohm  resistance. 

The  number  of  Watts  in  any  case  is  the  product  of  the  number  of 
volts  and  the  number  of  amperes,  or  the  product  of  the  number  of 
ohms  and  the  square  of  the  number  of  amperes.  Since  one  Watt  =  7^ 
horse-power,  the  horse-power  is  the  number  of  Watts  divided  by  746. 

QUESTIONS.— Explain  the  development  of  heat  in  a  current-carrying  Avire.  Sup- 
pose a  current  to  flow  through  a  wire  which  is  thicker  at  one  end  than  the 
other.  If  there  is  any  difference  in  the  strength  of  the  current  or  in  the  tem- 
perature at  the  two  ends  of  the  Avire,  state  the  difference  and  explain  it.  How 
many  heat-units  will  a  current  of  one  ampere  flowing  through  an  ohm  of  re- 
sistance generate  in  a  second  ?  If  the  current  is  doubled,  how  great  is  the 
heat  ?  Describe  a  calorimeter  used  for  measuring  heat  in  current-carrying 
\s-ires.  Suppose  the  resistance  of  a  Avire  to  be  07  ohm  and  a  current  of  10 
amperes  to  be  passed  through  it,  IIOAV  much  heat  \vill  be  liberated  each  second  ? 

Explain  heat-Avaste  in  AA'ires.  Ho\v  many  heat-units  are  developed  a  second  in  a 
copper  wire  •?&  of  an  inch  in  diameter,  when  carrying  a  current  of  ten  am- 
peres  ?  Convert  this  into  Avork-units  ;  into  horse-powers ;  into  Watts. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

How  would  you  determine  whether  the  electrification  of  a  substance  rubbed  with 
a  silk  handkerchief  is  positive  or  negative  ? 

A  piece  of  copper  wire  100  yards  long  weighs  a  pound  ;  another  piece  of  the  same 
wire  weighs  a  quarter.  Show  Avhat  are  the  relative  resistances  of  the  two. 

Can  the  power  of  electrical  attraction  be  developed  in  bodies  in  any  other  way 
than  by  friction  ? 

After  combing  your  hair  on  a  dry  day,  why  will  little  pieces  of  paper  adhere  for 
a  few  seconds  to  the  comb  ? 

Dip  a  piece  of  tourmaline  into  boiling  water  and  apply  it  to  your  gold-leaf  elec- 
troscope. Explain  what  happens  as  it  cools. 

Double  up  a  piece  of  pasteboard  and  tear  it  across  ;  either  piece  will  cause  the 
leaves  to  diverge.  Why  ?  Because  fracture  as  well  as  friction,  etc.,  produces 
electricity. 

Explain  why  it  is  that  if  you  walk  rapidly  over  a  carpeted  floor  on  a  clear,  cold 
day,  you  can  produce  a  spark  on  presenting  your  knuckle  to  any  metallic  ob- 
ject, or  to  the  face  or  hand  of  a  person  who  has  just  entered  the  room.  See 
whether  you  can  light  the  gas  by  means  of  this  spark. 

Why  is  dry  air  a  good  insulator  ?  Because  it  is  a  non-conductor ,'  otherwise  no 
body  would  remain  electrified  for  an  instant. 


504  ELECTRICITY. 

Is  a  vacuum  a  good  conductor  of  electricity  ? 

Enumerate  the  fundamental  facts  of  statical  electricity. 

Is  it  better  to  be  wet  or  dry  if  exposed  to  a  thunder-storm  ? 

What  parts  of  the  house  are  most  dangerous  during  such  a  storm  ? 

Is  the  electrical  discharge  accompanied  by  any  odor  ?    Describe  it. 

A  coil  of  wire  having  a  resistance  of  10  ohms,  carries  a  current  of  1-5  amperes. 
Required  the  difference  of  potential  on  its  ends.  Ans.  15  volts. 

An  electrometer  connected  on  the  terminals  of  an  electric  light  shows  a  potential 
difference  of  40  volts.  The  current  through  the  lamp  is  10  amperes.  What  is 
the  resistance  of  the  lamp  and  arc  between  the  terminals  ?  Ans.  4  ohms.  How 
much  heat  will  be  developed  in  the  lamp  and  arc  each  second  ?  Ans.  0-24x 
10a  x  4  =  96,  or  enough  to  heat  96  grammes  of  water,  1°  C. 

Has  the  velocity  of  electricity  ever  been  measured  ? 

The  velocity  of  electricity  depends  upon  the  conditions.  The  actual  velocity  of 
propagation  of  electro- magnetic  waves  in  space  is  the  same  as  that  of  light, 
about  186,000  miles  a  second.  The  velocity  of  transmission  of  signals  on  tele- 
graph lines  is  reduced  very  much  by  static  capacity  and  self-induction.  In  one 
instance  it  was  determined  to  be  16,000  miles  a  second  between  Washington 
and  St.  Louis  ;  and  in  submarine  cables  it  is  between  7,000  and  8,000  miles  a 
second. 

Why  are  not  birds  on  a  telegraph  wire  killed  by  the  passage  of  a  current  ? 

The  current  passing  through  a  telegraph  wire  is  not  injurious  to  birds  because  it 
does  not  leave  the  wire  ;  only  an  infinitesimal  portion  of  it  passes  into  the  body 
of  the  bird.  Should,  however,  a  bird  perched  on  a  wire  touch  with  any  portion 
of  its  body  a  second  wire  during  the  passage  of  an  electric  current,  the  current 
might  be  deflected  through  the  body  of  the  bird  with  fatal  consequences.  In- 
genious contrivances  have  been  devised  for  killing  mice  and  other  small  ani- 
mals by  making  a  connection  through  their  bodies. 

Do  any  animals  present  electric  currents  ? 

It  has  been  observed  that  all  living  muscles  are  traversed  by  electric  currents, 
which  are  more  marked  in  the  case  of  the  warm-blooded  animals,  and  are 
known  to  persist  for  a  time  after  death. 

Do  any  animals  possess  the  power  of  giving  an  electric  shock  ? 

Certain  fishes  are  provided  with  electric  organs  having  the  property  of  accumu- 
lating electric  force  and  communicating  it  in  shocks  to  other  animals.  Such 
are  the  electric  rays,  the  electric  cat-fish  of  the  Nile,  and  the  gymno'tus  or 
electric  eel,  the  latter  the  most  powerful  of  all.  The  gymnotus  inhabits  the 
marshy  regions  of  Brazil  and  Guiana,  where  it  attains  a  length  of  five  to  six 
feet.  It  is  an  object  of  terror  to  the  inhabitants,  for  the  discharge  of  its  bat- 
teries, which  are  planted  on  the  back  of  the  tail  and  along  the  anal  fin,  is  fatal 
to  the  largest  animals.  Certain  roads  are  said  to  have  been  abandoned  in  con- 
sequence of  the  number  of  horses  annually  killed,  while  crossing  swampy  depres- 
sions, by  eels.  The  electric  fishes  employ  their  singular  power  both  as  a  means 
of  self-defense  and  to  disable  or  kill  their  prey.  In  order  that  a  shock  may  be 
communicated  to  the  victim,  it  is  necessary  that  the  galvanic  circuit  should  be 
completed  by  connection  with  the  fish  at  two  distinct  points  ;  painful  sensations 
may  be  produced  even  by  a  discharge  conveyed  indirectly  through  the  medium 
of  water.  The  electric  currents  created  at  will  in  these  animals  have  not  been 
found  to  differ  in  their  properties  from  those  of  the  voltaic  cell,  in  that  they 
decompose  chemical  compounds,  charge  the  Leyden-jar,  render  the  needle 
magnetic,  and  even  yield  the  spark.  One  surface  of  the  electric  organ  is 
positive,  the  other  negative.  The  power  is  exhausted  after  several  discharges. 


FIG.  384.— ALTERNATING-CURRENT  DYNAMO. 


PRACTICAL   APPLICATIONS   OF 
ELECTRICITY. 

GENERAL   USEFUL  EFFECTS. 

Electricity  has  been  applied  to  so  many  Useful 
Purposes  that  it  has  become  one  of  the  most  important 
servants  of  mankind. 

The  Value  of  Electricity  for  Useful  Work  is  en- 
tirely due  to  the  fact  that  various  effects  can  be  produced 
by  it  with  the  greatest  convenience,  and  such  effects  are  usu- 
ally more  intense  than  those  due  to  any  other  agency.  The 
present  useful  effects  of  electricity  are  Magnetic,  Inductive, 
Lighting,  Heating,  and  Chemical.  These  are  produced  much 
better  by  electric  currents,  or  dynamic  electricity,  than  by 
frictional  or  static  electricity,  principally  because  the  latter 
33 


506    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

gives  only  an  instantaneous  effect,  like  a  spark,  while  the 
former  will  supply  energy  steadily  for  months  at  a  time. 


MAGNETIC  EFFECTS  OF  ELECTRICITY,   OR 
ELECTRO-MA  GNETISM. 

The  Electro-Magnet. — We  have  already  seen,  in  the 
case  of  the  galvanometer,  that  a  wire  or  coil,  carrying  a  cur- 
rent near  a  needle,  tends  to  make  the  needle  deflect  and  take 
a  position  at  right  angles  to  the  direction  of  the  current ; 
we  have  also  learned  that  this  effect  is  proportional  to  the 
number  of  turns  of  wire  passing  around  the  needle.  This 
very  important  discovery  of  the  action  of  an  electrical  cur- 
rent upon  a  magnetic  needle  was  made  by  Oerstedt  (or'sted), 
of  Copenhagen,  in  1819.  The  experiment  can  easily  be  re- 
peated by  simply  bringing  near  a  compass-needle  a  wire 
connected  with  one  or  two  cells  of  a  battery. 

If,  instead  of  using  a  magnetic  needle,  we  take  a  rod  of  soft 
wrought-iron,  we  shall  find  that  it  becomes  magnetized  when  held  at 

right  angles  to  a  wire  car- 
rying a  current,  although 
it  possessed  no  magnetic 
properties  beforehand.  We 
find  also  that  this  effect 
can  be  intensified  by  in- 
creasing the  number  of 
turns  of  wire  around  the 
bar,  and  in  this  way  we  can 
make  a  magnet  having  all 
the  properties  of  the  per- 
manent steel  magnet.  The 
magnetic  action,  however, 
is  only  temporary,  and 
ceases  almost  entirely  as  soon  as  the  wire  carrying  the  current  is  re- 
moved, or  the  current  stopped. 

Such  magnets  are  called  electro-magnets,  and  usually  consist  of 
two  wrought-iron  cylindrical  cores  joined  by  a  wrought-iron  yoke,  gen- 
erally attached  to  the  cores  by  screws,  as  shown  in  Fig.  385.  Around 


FIG.  3&5.—  ELECTRO-MAGNET. 


CONSTRUCTION  OF  ELECTRO-MAGNET.  507 

each  core  a  number  of  turns  of  wire  are  wound,  forming  what  are 
called  the  coils,  spools,  helices,  or  bobbins. 

The  coils  should  be  wound  or  connected  so  that  the  current  passes 
around  one  core  in  one  direction,  and  around  the  other  in  the  opposite 
direction,  in  order  that  one  shall  form  a  north  pole  and  the  other  a 
south  pole ;  and  the  rule  is,  that  the  current  should  flow  around  the 
north  pole  in  a  direction  opposite  to  that  of  the  hands  of  a  watch,  if  we 
imagine  the  watch  and  the  end  of  the  core  both  to  face  us.  A  bar  of 
soft  iron  is  used  as  an  armature,  and  is  very  powerfully  attracted  when 
a  strong  current  is  passed  through  the  coils ;  but  this  magnetic  effect 
continues  only  so  long  as  the  current  flows,  and  the  instant  the  circuit 
is  broken  the  attraction  ceases  almost  entirely.  The  slight  effect  whiob 
remains  is  called  residual  magnetism,  and  is  similar  to  the  retentivity 
or  coercive  force  of  permanent  magnets.  Since  this  residual  magnetism 
is  hardly  perceptible  in  very  soft  wrought-iron,  but  is  very  strong  in 
hard  steel,  and  since  a  certain-sized  electro-magnet  of  soft  iron  can  be 
made  to  exert  a  much  stronger  attraction  than  one  of  steel,  the  softest 
and  best  quality  of  soft  iron  should,  therefore,  be  used  in  the  construc- 
tion of  electro-magnets." 

A  magnetic  effect  may  be  obtained  from  a  coil  of  wire  carrying  a 
current,  even  though  the  coil  has  no  iron  core  within  it.  Such  a  coil 
without  a  core  is  called  a  solenoid,  and  is  sometimes  used  instead  of  an 
electro-magnet.  The  magnetic  effect  is,  however,  very  much  weaker 
if  there  be  no  iron  core,  the  presence  of  iron  tending  greatly  to  concen- 
trate and  conduct  the  magnetic  lines  of  force. 

Electro-magnets  are  almost  always  used  instead  of  permanent 
magnets,  because  their  action  is  controllable  and  much  more  powerful. 

The  Practical  Applications  of  Electro-Magnetism 

are  many — in  fact,  electro-magnets  form  part  of  almost  all 
useful  electrical  apparatus.  The  first  of  these  applications 
that  was  developed  is 

The  Electro-Magnetic  TelegTaph.  —  The  simplest 
system  of  telegraphy,  and  the  one  most  extensively  used,  is 
that  invented  in  1837  by  S.  F.  B.  Morse,  an  American.  The 
Morse  apparatus  consists  essentially  of  an  electro-magnet, 
which,  when  a  current  passes  through  its  coils,  attracts  an 
armature.  In  this  way  an  operator  can  cause  the  armature 
to  move,  even  at  a  distant  station,  by  simply  sending  a  cur- 
rent over  a  wire  leading  to  that  station. 


508    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

The  instrument  by  which  the  sending  operator  controls  the  current 
on  the  line  is  called  a  key,  and  is  shown  in  Fig.  386.  It  consists  simply 
of  a  platinum  con- 
tact-point, mount- 
ed on  a  lever,  which 
closes  the  electric 
circuit  when  the 
knob  on  the  for- 
ward end  of  the  lever  is  depressed. 
By  means  of  this  key,  the  operator 
sending  the  message  can  cause  a 

current  to  flowover  the  wire  through 

.   .          .  FIG.  386.— MORSE  TELEGRAPH  KEY. 

the    receiving    instrument    at    the 

other  end,  either  for  a  short  or  long  interval,  and  the  motion  of  the 
armature  of  the  distant  receiving  instrument  will  correspond  exactly 
with  that  of  the  sending  key. 

The  receiving  instruments  are  of  two  kinds,  the  most  common  be- 
ing the  "  sounder  "  (Fig.  387),  which  consists  of  an  electro-magnet  fixed 
vertically  upon  a  flat  base.  The  armature,  which  is  a  strip  of  soft  iron, 
is  mounted  horizontally  immediately  above,  but  not  touching,  the  poles 


FIG.  387.— TELEGRAPH  SOUNDER. 


of  the  magnet,  and  at  the  middle  of  a  lever  pivoted  at  one  end.  Screws 
are  provided  at  the  other  end  of  the  lever  to  regulate  its  up  and  down 
movements,  and  there  is  also  an  adjustable  spring  which  always  tends 
to  draw  the  armature  up. 


TELEGRAPH  REGISTER.  509 

When  a  current  is  passed  through  the  magnet,  the  armature  is 
drawn  down,  causing  a  click ;  and,  when  the  current  is  stopped,  the 
armature  is  pulled  back  by  the  spring,  causing  another  click. 

The  other  kind  of  receiving  instrument  is  the  register  shown  in 
Fig.  388.  Here  the  armature  causes  marks  to  be  made  on  tape,  which 
is  slowly  moved  by  clock-work. 
If  the  current  sent  over  the  wire 
lasts  only  for  an  instant,  a  dot  is 
impressed  on  the  tape ;  but,  if  the 
current  is  continued,  a  dash  ap- 
pears. The  marks  are  made  on 


FIG.  388.— MORSE  TELEGRAPH  REGISTER. 

the  tape  either  by  simply  indenting  the  paper  with  a  sharp  point  or 
stylus  on  the  end  of  the  pivoted  lever  carrying  the  armature,  or  by 
means  of  some  form  of  pen  fed  with  ink. 

The  Alphabet,  or  Code  of  Signals,  by  which  messages 
are  sent,  is  composed  of  different  combinations  of  dots  and 
dashes — that  is,  short  or  long  impulses  of  current  over  the 
line.  The  code  used  in  this  country,  presented  on  the  next 
page  for  reference,  is  the  one  originally  devised  bj  Professor 
Morse.  The  different  signals  are  carefully  selected,  so  that 
those  used  most  frequently  are  the  shortest,  A  slightly 
different  code  is  employed  in  Europe.  This  was  intended 
to  be  an  improvement  on  the  original  Morse  alphabet,  but 
the  European  code  has  been  found  to  require  more  time  to 
send  a  given  message. 


510    PRACTICAL   APPLICATIONS  OF  ELECTRICITY. 


MORSE   CODE   OF    SIGNALS. 


A  -  — 

B 

C  --  - 

D 

E  - 

F 

G 


H 

I    -- 

J 

K 

L  - 
M  — 
N  — - 


R  -  -- 
S  --- 
T  - 
U 


NUMERALS. 

5 


Period         

Comma       

Semicolon 


PUNCTUATION. 

Interrogation  —  -  -  —  - 

Exclamation 

Parenthesis     


Paragraph 

Italics          


It  should  be  carefully  noted  that  0  differs  from  I  in  that  the  two 
dots  are  farther  apart ;  L  is  twice,  and  the  cipher  three  times,  as  long 
as  T.  C  and  R  differ  from  S  and  from  each  other  by  being  differently 
spaced.  The  same  is  true  of  H,  Y,  Z.  etc.  Skilled  operators  experi- 
ence no  difficulty  in  making  these  distinctions. 

The  Relay. — In  the  case  of  a  long  line,  or  where  there 
are  a  number  of  instruments  on  one  circuit,  the  current  may 


FIG.  389. —TELEGRAPH  RELAY. 

not  have  sufficient  strength  to  work  the  receiving  instru- 
ments directly ;  in  such  a  case,  a  relay  or  repeater  is  used. 
The  regular  form  of  relay  is  shown  in  Fig.  389.  It  consists 
of  an  electro-magnet  and  pivoted  lever  carrying  the  armature, 
similar  to  the  sounder ;  but  in  the  relay  a  great  many  turns 
of  very  fine  wire  are  used,  in  order  to  multiply  the  effect  of 


A  TELEGRAPH  CIRCUIT. 


511 


a  weak  current.  The  armature  and  lever  are  also  made  very 
light,  so  as  to  work  easily ;  and  a  platinum  contact-point, 
similar  to  that  on  the  key,  is  mounted  on  the  end  of  the 
lever,  so  that,  when  the  armature  is  drawn  forward,  a  local 
circuit,  in  which  are  included  a  local  battery  and  the  receiv- 
ing sounder  or  register,  is  closed.  The  object  of  the  relay 
is,  therefore,  to  re-enforce  with  a  strong  local  current  any 
current  too  weak  to  do  the  required  work  itself. 

The  connections  for  the  regular  Morse  circuit  for  one  intermediate 
and  two  terminal  stations  are  shown  in  the  diagram  (Fig.  390).  If  we 
trace  out  the  connections  in  this  diagram,  we  find  that  when  the  key 
K  at  the  station  A  is  depressed,  it  will  send  a  current  over  the  line 


FIG.  390.— A  MORSE  TELEGRAPH  CIRCUIT. 

from  the  main  battery,  M  B,  causing  the  armatures  of  all  three  of  the 
relays,  R,  R2,  R3,  to  be  drawn  forward.  This  will  close  the  local  cir- 
cuit at  each  station,  and  the  local  batteries,  Ib,  lb*,  lb3,  will  cause  the 
armatures  of  the  three  sounders,  S,  S2,  S3,  to  move  simultaneously  in 
perfect  correspondence  with  the  motions  of  the  sending  key  K.  It 
will  be  noticed  that  the  wire  is  carried  to  the  plate  G  in  the  earth  at 
each  end  of  the  line.  By  this  means  the  earth  is  made  to  act  as  the 
return  conductor  to  complete  the  circuit,  and  it  is  thus  necessary  to 
have  only  one  wire,  which  effects  a  great  saving  on  long  lines.  The 
keys  are  all  kept  closed  except  when  used  in  telegraphing. 

Faults  may  occur  in  Telegraph  Lines  from  a  num- 
ber of  causes :  First,  the  wires  may  break,  which,  of  course, 
entirely  interrupts  the  signaling;  secondly,  the  insulators 
may  break  or  become  imperfect,  so  that  the  current  on  the 
wire  leaks  off  to  the  earth  before  it  reaches  the  distant  sta- 
tion, and  thus  weakens  the  effect ;  or,  thirdly,  two  wires  may 


512    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

come  in  contact  with  each  other  and  cause  a  mixing  of  the 
signals.     This  last  fault  is  called  a  "  cross." 

Various  methods  for  testing  the  existence  and  positions 
of  faults  are  used  by  telegraph  engineers.  They  usually 
depend  upon  accurate  measurements  of  resistance  or  ca- 
pacity (see  page  485). 

Duplex  Telegraphy. — There  are  several  methods  of 
arranging  telegraphic  apparatus  so  as  to  transmit  two  mes- 


FIG.  391.— DUPLEX  TELEGRAPH  CIRCUIT. 

sages  through  one  wire  at  the  same  time.  One  of  these 
methods  of  duplex  working  is  called  the  Wheatstone  Bridge 
method.  Fig.  391  illustrates  the  principle.  All  that  is 
necessary  in  a  duplex  system  is  that  the  receiving  instru- 
ment at  each  end  should  move  only  in  response  to  signals 
from  the  other  end,  so  that  an  operator  at  A  may  cause  the 
receiving  instrument,  S,  to  work  without  affecting  his  own 
receiving  instrument,  T.  The  same  must  be  true  from  the 
other  end  also.  In  order  to  accomplish  this,  the  circuit  at 
each  end  is  divided  into  two  branches,  one  of  which  con- 
nects with  the  earth  and  the  other  with  the  line,  and  the  re- 
ceiving instrument  is  placed  across  between  these  branches. 

Now,  by  the  principle  of  the  Wheatstone  Bridge,  if  the  resistance 
in  F  is  to  the  resistance  in  Z  as  the  resistance  of  the  line  is  to  the  re- 
sistance of  H,  then  no  current  will  flow  through  the  instrument  when 
the  key  at  A  is  closed ;  but  if  a  current  be  sent  from  the  other  end,  B, 
a  portion  of  this  current  will  flow  through  the  receiving  instrument, 
T,  and  cause  it  to  work.  In  this  way,  signals  can  be  sent  at  the 


SUBMARINE  TELEGRAPHY. 


513 


time  from  both  ends,  which  will  operate  the  receiving  instruments  at 
the  opposite  ends  of  the  line,  but  will  not  affect  the  instruments  at  the 
ends  from  which  they  are  sent. 

Multiplex  Telegraphy. — By  a  further  extension  of  the 
principle  of  duplex  telegraphy,  it  is  possible  to  send  four 
messages  on  a  wire  at  the  same  time,  and  some  ingenious 
methods  have  been  invented  by  means  of  which  it  is  possible 
to  send  seventy-two  distinct  messages  on  the  same  wire  at  the 
same  time ;  but,  of  course,  such  systems  are  extremely  com- 
plicated, and  practically  useless. 

Learner's  Instruments. — A  simple  but  complete  tele- 
graphic apparatus  is  shown  in  Fig.  392.  Such  instruments 


FIG.  392.— LEARNER'S  TELEGRAPHIC  OUTFIT. 

are  quite  cheap,  and  enable  the  pu- 
pil to  learn  how  to  send  and  re- 
ceive telegraphic  messages.  They 
may  even  be  used  on  short  lines, 
up  to  about  one  mile  in  length. 

Submarine      Telegraphy. — 

The  methods  of  telegraphing  be- 
tween places  separated  by  water  are  very  similar  to  those  em- 
ployed on  land  lines ;  but  in  the  case  of  submarine  teleg- 
raphy several  serious  difficulties  are  encountered,  which 
make  it  necessary  to  use  more  nearly  perfect  lines  and  in- 
struments. In  the  first  place,  if  a  telegraph  wire  is  laid 
under  water,  it  must  be  perfectly  insulated  throughout 


514    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

its  length  with  some  non-conducting  and  water-proof  cov- 
ering; otherwise  the  current  used  in  telegraphing  would 
all  leak  off  the  wire  in  a  very  short  distance.  Submarine 
cables,  therefore,  consist  of  a  core  or  conductor  proper, 
made  of  several  (usually  seven)  copper  wires  twisted  to- 
gether in  order  to  be  flexible.  This  core  is  covered,  first 
with  a  stout  layer  of  gutta-percha,  then  with  a  woven  coat- 
ing of  jute,  and  finally  with  a  sheathing  or  armor  of  ten 
iron  wires,  each  covered  with  hemp.  These  are  wound  on 
the  outside,  and  give  the  finished  cable  the  appearance  of 
a  rope  about  one  inch  in  diameter. 

The  strength  of  the  cable  depends  upon  this  armor ;  and  the  breaks 
in  cables,  which  so  often  occur  and  cause  so  much  trouble  and  ex- 
pense, are  almost  always  due  to  the  failure  of  this  armor  to  stand  the 
severe  pull  and  scraping  to  which  the  cable  is  subjected. 

Another  serious  difficulty  in  submarine  telegraphy  is  the  fact  that 
a  cable  acts  as  an  enormous  Leyden-jar.  which  requires  a  large  quan- 
tity of  electricity  to  charge  it.  When  a  current  is  sent  over  the  cable, 
the  current  has  to  fill  the  cable,  as  it  were,  before  it  can  work  the  re- 
ceiving instrument  at  the  other  end.  This  effect,  which  is  called 
Static  Induction,  greatly  reduces  the  speed  of  signaling  through 
cables,  so  that  not  half  as  many  words  can  be  sent  per  minute  as  on 
ordinary  land  lines. 

The  existence  of  static  induction  also  makes  it  necessary  to  use 
extremely  sensitive  instruments  to  receive  the  signals ;  in  fact,  it  was 
for  this  purpose  that  Sir  William  Thomson  devised  his  mirror  galva- 
nometer, which,  we  have  seen,  is  also  used  in  laboratories  for  measur- 
ing very  weak  currents.  The  motion  of  a  spot  of  light  reflected  from 
the  mirror  enables  the  receiving  operator  to  read  the  signals  sent. 

Electric  Bells. — In  many  cases  where  it  is  not  desired 
to  send  messages  over  a  wire,  but  merely  to  make  a  sound 
to  attract  attention,  electric  bells  are  used.  They  consist  of 
an  electro-magnet  and  a  pivoted  lever  carrying  an  armature 
similar  to  the  sounder ;  but  the  lever  is  arranged  to  strike 
the  bell  when  the  armature  is  drawn  forward,  instead  of 
merely  striking  the  screw-point.  In  order  to  operate  an  elec- 
tric bell,  all  that  is  necessary  is  to  send  a  current  through 
the  coils  of  its  electro-magnet.  The  usual  means  employed 


ELECTRIC   BELLS. 


515 


for  closing  the  circuit  is  a  "  push-button,"  which  is  merely 
a  small  spring  contact-point. 

The  bell  above  described  is  what  is  known  as  a  single-stroke  bell, 
since  it  sounds  but  once  each  time  the  push-button  is  pressed.  The 
continuous-ringing  electric  bell,  which  is  the  one  generally  used,  be- 
cause it  has  the  advantage  of  keeping 
up  the  ringing  as  long  as  the  button 
remains  pressed  down,  is  shown  in  Fig. 
393.  It  differs  from  the  bell  already 
described  in  that  the  circuit  passes 
through  the  lever  which  strikes  the 
bell.  When  the  armature  is  drawn 
forward,  it  breaks  the  circuit  at  the 
contact-point  shown  on  the  back  of 
the  armature.  This  allows  the  arma- 
ture to  drop  back,  after  having  struck 
the  bell.  The  action  is  then  repeated, 
causing  a  vibration  and  continuous 
ringing  as  long  as  the  push-button  is 
pressed. 

Such  electric  bells  are  used  for 
many  purposes,  as  door-bells,  call-bells, 
and  burglar-alarm  bells.  In  the  burg- 
lar-alarm, the  push-button  is  replaced 
by  a  contact-point  on  the  door  or  win- 
dow, so  arranged  that  when  the  door 
or  window  is  opened,  the  circuit  is 

closed  and  the  bell  rings.  An  attachment  is  often  added  by  means 
of  which  the  bell,  once  started  by  opening  the  window,  will  continue 
to  ring  after  the  window  has  been  shut  down  again ;  otherwise,  the 
ringing  might  not  last  long  enough  to  give  sufficient  alarm. 

Electric  Clocks. — Another  very  similar  application  of 
electricity  is  the  electric  clock,  the  simplest  form  of  which 
consists  merely  of  one  or  two  hands  that  are  caused  to  move 
around  by  means  of  an  electric  magnet.  The  hands  advance 
by  what  is  called  a  "  step-by-step  motion "  each  time  an 
electrical  impulse  is  sent  over  the  wire  from  the  standard 
clock.  The  circuit  is  closed  once  every  second.  One  mas- 
ter-clock, as  it  is  called,  may  operate  a  number  of  electric 


FIG.  393. — ELECTRIC  BELL. 


516    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

clocks  placed  around  at  diff-erent  points  on  the  same  circuit 
It  is  in  this  way  that  standard  time  is  sent  over  the  country 
from  the  observatory  at  Washington  or  other  important 
astronomical  observatories. 

QUESTIONS.— Explain  the  value  of  electricity  for  performing  work.  Enumerate 
the  useful  effects.  Explain  the  principle  of  the  Electro-magnet.  What  is  a 
solenoid  ?  Why  are  electro-magnets  preferable  to  permanent  magnets  ?  De- 
scribe the  Morse  system  of  Telegraphy  ;  the  key,  and  its  object ;  the  sounder  ; 
the  Morse  telegraph  register.  Explain  the  relay,  and  state  its  object.  Draw  a 
diagram  illustrating  a  Morse  telegraph  circuit. 

How  can  two  messages  be  transmitted  through  one  wire  at  the  same  time  ?  Ex- 
plain the  Wheatstone  Bridge  method.  How  may  the  principle  of  duplex  teleg- 
raphy be  extended  ?  What  difficulties  are  encountered  in  submarine  teleg- 
raphy ?  Of  what  do  submarine  cables  consist  ?  Why  are  extremely  sensitive 
instruments  required  to  receive  the  signals  ?  When  was  the  first  telegraph 
line  built  ?  In  1844,  between  Baltimore  and  Washington.  How  many  miles  of 
telegraph  line  are  there  now  in  the  world  ?  Nearly  800,000.  The  electric  wire 
in  operation  in  New  York  City  alone  is  long  enough  to  encircle  the  earth  three 
times  at  the  equator. 

Describe  the  single-stroke  Electric  Bell ;  the  continuous-ringing  bell.  For  what 
purposes  are  electric  bells  used  ?  What  are  Electric  Clocks  ?  Describe  their 
method  of  operation. 


INDUCTIVE  EFFECTS  OF  ELECTRICITY. 

Electro-Magnetic  Induction. — We  have  already  seen 
that  a  charge  of  electricity  has  the  power  to  induce  another 
charge  in  a  body  near  it.  This  is  called  Electrostatic  In- 
duction. In  the  case  of  dynamic  or  current  electricity,  we 
also  find  that,  when  a  magnet  is  moved  near  a  wire,  a  cur- 
rent of  electricity  will  be  produced  in  the  wire ;  or  if  an 
electro-magnet  is  suddenly  excited  by  sending  a  current 
through  its  coils,  a  current  will  be  produced  in  a  wire  or 
coil  near  the  electro-magnet.  In  fact,  any  change  whatever 
in  the  position  or  the  strength  of  a  magnet  will  tend  to  pro- 
duce a  current  in  a  neighboring  wire  or  coil. 

The  explanation  of  this  phenomenon  is  usually  expressed,  accord- 
ing to  the  views  of  Faraday,  by  saying  that  the  magnetic  lines  of 
force  cut  the  wires  or  the  wires  cut  the  lines  of  force,  which  is  the 
same  thing.  These  lines  of  force  are  imaginary  ones,  which  for  con- 
venience we  assume  to  represent  the  magnetic  force  of  attraction  in 


ELECTRO-MAGNETIC  INDUCTION. 

the  neighborhood  of  a  magnet.  An  idea  of  these  lines  has  already 
been  given  in  the  case  of  the  magnetic  figures  made  of  iron-filings 
(page  429).  We  have  also  seen  that  an  electric  current  always  has 
magnetic  effects,  and  will  turn  a  compass-needle.  Therefore,  when  we 
move  a  coil  carrying  a  current  or  vary  the  strength  of  the  current  in 
the  wire,  we  shall  produce  a  current  by  induction  in  the  neighboring 
wire  or  coil.  Thus  we  see  that  any  magnetic  change  tends  to  produce 
an  electric  current  in  a  wire  in  the  neighborhood ;  but  it  must  be  borne 
in  mind  that  a  change  of  some  kind  is  necessary.  The  mere  presence 
of  a  magnet  near  a  wire  produces  no  effect  whatever  unless  the  magnet 
is  moved  or  changed  in  strength. 

It  is  possible  to  illustrate  the  above  facts  by  very  simple  experi- 
ments.   All  that  is  necessary  is  to  make  a  coil  of  insulated  wire,  say  of 
30  to  40  turns  and  two  or 
three  inches  in  diameter,  the 
ends  of  which  are  connected 
with  a  galvanometer.     A  gal- 
vanometer may  be  improvised 
with  a  pocket  compass,"  or  a 
magnetized  piece  of  knitting- 
needle  suspended  on  a  thread  FIG.  394.— INDUCTION  EXPERIMENT. 
and  surrounded  by  a  coil  of 

30  or  40  turns  of  insulated  wire.  If  a  magnet  is  now  thrust  into  the 
first  coil  or  brought  near  it,  the  needle  of  the  galvanometer  will  swing, 
showing  that  a  current  is  generated  in  the  coil.  In  fact,  with  a  deli- 
cate galvanometer  it  will  be  very  difficult  to  move  either  the  coil  or 
the  magnet,  even  when  they  are  a  yard  apart,  without  affecting  the 
galvanometer-needle.  If  the  magnet  is  replaced  by  a  coil  of  wire  con- 
nected with  one  or  two  cells  of  a  battery,  a  similar  set  of  experiments 
will  show  the  induction  currents  made  by  the  motion  or  variation  of 
another  current. 

This  electro-magnetic  inductive  action  is  of  the  utmost 
scientific  and  practical  importance,  since  many  of  the  use- 
ful applications  of  electricity  are  based  directly  upon  it. 
For  example,  the  dynamo-electric  machine,  the  electric 
motor,  and  the  telephone,  are  all  apparatus  for  producing 
and  using  inductive  action.  The  simple  experiments  sug- 
gested above  will  greatly  aid  the  pupil  in  clearly  understand- 
ing the  principles  of  these  machines,  which  are  the  three 
most  important  pieces  of  electrical  apparatus. 


518    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 


Fia.  395.— THE  INDUCTION  COIL. 


The  Induction  Coil  consists  of  an  iron  core  surrounded 
by  a  coil  usually  made  of  three  or  four  layers  of  coarse  wire, 
the  ends  of  which  are  brought  out  to  binding-posts.  Outside 
of  this  coil  there  is  a  second  coil,  usually  consisting  of  a  great 

many  turns  of  fine 
wire ;  the  ends  of  this 
coil  are  also  led  to 
binding  -  posts.  The 
pupil  may  easily  con- 
struct a  coil  of  any  de- 
sired size.  The  core 
should  be  made  of  a 
bundle  of  iron  wire 
surrounded  by  stout 
paper  and  having 
square  pieces  of  board 
about  an  inch  thick 
at  each  end  to  hold 
the  wire  in  place.  The  action  of  this  coil  is  nothing  more 
than  the  simple  inductive  action  already  described.  When 
the  current  from  a  few  cells  of  a  battery  is  caused  to  pass 
through  the  coil  of  coarse  wire  called  the  primary  coil,  a 
current  is  produced  in  the  secondary  coil  of  fine  wire,  be- 
cause the  passage  of  the  primary  current  makes  the  iron 
core  strongly  magnetic. 

Since  this  inductive  action  is  exerted  on  each  turn  of  wire  in  the 
secondary  coil,  it  is  evident  that  the  total  effect  obtained  from  a  large 
number  of  connected  turns  must  be  very  marked,  and  this  we  find  to 
be  the  fact.  It  is  possible  to  obtain,  from  a  comparatively  small  coil, 
sparks  one  quarter  of  an  inch  long  when  two  or  three  cells  are  used  on 
the  primary  circuit,  whereas  the  cells  alone  would  not  be  able  to  make 
a  spark  one  thousandth  of  an  inch  in  length.  With  a  large  induction 
coil  we  can  increase  the  tension  or  jumping  power  to  such  an  extent 
that  we  may  cause  the  induced  current  to  run  round  a  theatre  and  light 
hundreds  of  gas-burners.  Very  large  induction  coils  have  been  made 
with  as  many  as  3,000  or  4,000  turns  of  wire  in  the  secondary ;  some 
of  them  give  a  spark  four  or  five  feet  long. 


THE  TELEPHONE.  519 

A  spark  is  produced  by  an  induction  coil  each  time  the 
primary  circuit  is  closed  or  opened.  The  multiplication 
of  effect  is,  however,  only  in  the  tension  (designated  as  E. 
M.  F.,  electro-motive  force)  of  the  current,  and  the  -actual 
energy  in  the  secondary  circuit  can  not  be  greater  than  that 
in  the  primary  circuit.  It  will  probably  be  considerably 
less,  because  of  various  losses.  All  we  accomplish  is  to  get  a 
very  much  higher  E.  M.  F.  (measured  in  volts)  than  we  have 
in  the  primary  circuit,  while  the  actual  current  of  the  sec- 
ondary (measured  in  amperes)  is  much  less  than  that  of  the 
primary.  In  short,  we  simply  transform  the  electricity,  and 
for  many  purposes  this  change  of  E.  M.  F.  is  desirable. 

It  is  usual  in  induction  coils,  also  called  Ruhm'korff  coils,  to  have 
some  mechanical  arrangement  run  by  clock-work  for  opening  and 
closing  the  primary  circuit ;  or  we  may  use  an  "  electric  buzzer,"  work- 
ing on  the  same  principle  as  the  continuous-ringing  electric  bell,  and 
applied  to  the  end  of  the  iron  core  of  the  induction  coil. 

The  Telephone. — The  transmission  of  speech  by  elec- 
tricity is  effected  by  means  of  an  instrument  called  the  Tele- 
phone, which  depends  entirely  upon  induction  for  its  action. 
The  ordinary  Bell  telephone,  an  extremely  simple  instru- 
ment, shown  in  section  and  in  perspective  in  Fig.  396,  con- 
sists of  a  magnet,  M,  having  at  one  end  a  coil  of  very  fine 
wire,  S,  and  a  sheet-iron  diaphragm,  Gr  G,  close  to,  but  not 
in  contact  with,  the  magnet.  These  three  parts — the  mag- 
net, coil,  and  diaphragm — are  really  all  that  is  essential  to 
the  telephone.  They  are  contained  in  a  wooden  case,  F, 
having  a  mouth-piece,  E.  The  connections  from  the  two 
ends  of  the  coil  S  are  carried  by  two  wires,  C  C,  to  two  bind- 
ing-posts, D  D,  at  the  other  end  of  the  instrument. 

In  order  to  use  the  telephone,  we  need  simply  connect  two  instru- 
ments in  a  complete  electric  circuit.  Then,  when  we  speak  into  the 
mouth-piece,  the  diaphragm  will  be  made  to  vibrate  by  the  sound,  and 
its  motion  near  the  magnet,  M,  will  cause  variation  in  the  lines  of 
magnetic  force,  which  we  know  will  produce  electric  currents  in  the 
coil  S.  These  currents  will  flow  over  the  wires  to  the  other  telephone  at 


520    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

the  opposite  end  of  the  line,  where  they  will  in  turn  change  the 
strength  of  the  magnet,  causing  the  diaphragm  of  the  second  tele- 
phone to  move  in  perfect  unison  with  that  of  the  first.  Thus  we  see 


FIG.  396.— THE  BELL  TELEPHONE  IN  SECTION  AND  PERSPECTIVE. 

that  the  sound-waves  of  the  voice  are  turned  into  electrical  waves  in 
the  first  telephone,  from  which  they  travel  over  the  wires  to  the  second 
telephone,  to  be  converted  back  into  sound-waves.  The  action  is  so 
nearly  perfect  that  it  is  possible  to  recognize  a  familiar  voice.  The 
Bell  telephone  may  be  employed  in  this  way  either  as  a  "  receiver  "  or 
"  transmitter,"  but  ordinarily  it  is  used  only  for  receiving. 

The  Usual  Form  of  Transmitting-  Telephone  is  that 
invented  by  Edison  and  Blake.  It  consists  simply  of  a 
carbon  button  in  contact  with  a  diaphragm,  and  a  contact- 
point  through  which  the  electric  circuit  is  carried. 

When  the  diaphragm  vibrates,  it  varies  the  pressure  on 
the  contact-point,  changing  the  resistance  to  the  passage  of 
the  current,  and  producing  waves  of  current  in  the  circuit 
corresponding  to  the  vibrations  of  the  diaphragm. 


A  TELEPHONE  CIRCUIT. 


521 


LINE 


The  connections  for  this  kind  of  telephone  are  shown  in  Fig.  397, 
in  which  C  is  the  carbon  button  mounted  on  a  spring ;  D  is  the  dia- 
phragm ;  and  F  is  the  contact-point,  placed  between  the  two  and  in 
contact  with  both.  The  button  is  connected  with  the  line  wire  which 
runs  through  the  receiving  instrument,  R,  and  then  to  the  earth,  re- 
turning through  the  earth  to  the  starting-point,  where  it  passes 
through  the  battery,  B, 
and  back  to  the  con- 
tact-point, C.  This 
arrangement  gives  a 
stronger  effect  than 
two  Bell  telephones, 
but  has  the  disadvan- 
tage of  requiring  a  bat- 
tery, whereas  a  Bell 
telephone  used  as  a 
transmitter  needs  no 
battery,  since  it  gener- 
ates its  own  current 
by  induction. 

A  still  further  ap- 
plication of  the  princi- 
ple of  induction  is  usu- 
ally made  in  practice 
by  passing  the  current 
from  the  transmitter 
through  the  primary  P 
of  an  induction  coil,  as 
shown  in  the  lower  dia- 
gram of  Fig.  397.  The 
current  obtained  from  the  secondary  coils,  S  S,  is  carried  by  the  line 
wire  to  the  receiving  instrument  at  the  other  end.  In  this  way,  the 
E.  M.  F.  of  the  current  is  raised  so  that  the  current  is  more  easily 
carried  over  the  wire,  and  the  effect  of  the  variable  resistance  of  the 
contact-point  is  relatively  greater  than  if  no  induction  coil  were  added. 

The  electric  bells  commonly  used  with  telephones  are  merely  for 
signaling  or  calling  up,  and  have  nothing  to  do  with  the  transmission 
of  speech. 

The  Microphone  is  precisely  the  same  in  action  as  the 
transmitting  telephone,  it  being  really  nothing  more  than  a 
loose  contact-point  consisting  of  two  pieces  of  carbon  lightly 
34 


FIG.  397.— TELEPHONE  CIRCUIT. 


522     PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 


touching  each  other,  and  included  in  a  circuit  with  one  or 
two  cells  of  a  battery  and  a  Bell  telephone.  The  slightest 
vibration  will  jar  the  contact  and  vary  its  resistance,  pro- 
ducing a  sound.  For  instance,  the  ticking  of  a  watch  is 
distinctly  heard,  and  even  the  footfalls  of  an  insect  under 
favorable  conditions  will  produce  vibration  enough  to  make 
a  sound  in  the  telephone. 

The  Dynamo-Electric  Machine  is  the  most  important 
of  all  electrical  apparatus,  as  it  is  the  generator  or  source 
from  which  ninety-nine  per  cent  of  all  the  electricity  now 

used  is  obtained.  It  is 
practically  necessary  for 
any  one  who  wishes  to 
employ  a  considerable 
amount  of  electricity, 
for  any  purpose,  either 
to  have  a  dynamo  on 
the  spot,  or  else  to  bring 
the  electricity  over  a 
wire  from  some  supply- 
station  where  dynamos 
are  kept  running.  In 
the  experiment  illustrat- 
ing electro-magnetic  induction,  it  was  shown  that,  when  a 
wire  is  moved  in  the  neighborhood  of  a  magnet,  an  electric 
current  is  generated  in  the  wire.  This  is  the  essential  prin- 
ciple of  the  dynamo-machine — in  fact,  a  wire  caused  to  move 
near  a  magnet  is  an  elementary  form  of  dynamo. 

The  power  of  the  current  obtained  by  this  inductive 
action  depends :  1.  Upon  the  strength  of  the  magnet ;  2. 
Upon  the  length  or  number  of  turns  of  wire ;  3.  Upon  the 
speed  of  the  motion ;  4.  Upon  the  conductivity  of  the  wire. 
The  particular  means  used  to  secure  these  conditions  are 
different  in  each  machine,  and  hundreds  of  different  forms 
have  been  invented.  The  common  dynamo,  however,  is 


FIG.  398.— THE  GRAMME  RING  ARMATURE. 


THE  DYNAMO-ELECTRIC  MACHINE.  523 

simply  a  coil  or  series  of  coils  of  wire,  known  as  the  armature, 
revolving  between  the  poles  of  a  powerful  electro-magnet, 
called  the  "  field  magnet,"  which  produces  the  magnetic 
field  in  which  the  armature  revolves. 

The  Gramme  King-. — There  are  two  principal  types  of 
armature  used  in  dynamos.  The  first  is  called  (from  the 
name  of  its  French  inventor)  the  Gramme  Eing,  and  con- 
sists of  a  ring  of  iron  wound  around  with  wire,  which  virtu- 
ally forms  one  endless  coil.  Connections  are  made  with  this 
coil  at  various  points,  each  of  which  is  in  communication 
with  a  number  of  insulated  copper  bars,  made  into  a  cylin- 
der called  the  "  commutator."  Now  suppose  this  ring  arma- 
ture to  revolve  between  the  poles  of  a  magnet ;  then  one  side 
of  the  ring  will  be  acted  upon  by  the  north  pole  and  the 
other  side  by  the  south  pole,  and  currents  will  be  produced 
in  the  wire  in  one  direction  on  one  side  of  the  ring,  and  in 
the  opposite  direction  on  the  other.  These  currents  will 
meet  in  the  middle,  either  at  the  top  or  bottom  of  the  ring, 
if  the  poles  of  the  field  magnet  are  on  each  side.  If  two 
conducting  brushes  are  placed  in  contact  with  the  upper 
and  lower  points  of  the  commutator,  respectively,  the  cur- 
rents produced  in  the  two  sides  of  the  ring  will  unite  and 
flow  out  of  one  brush  through  any  circuit  which  may  be 
provided,  and  back  to  the  armature  through  the  other  brush. 
This  action  is  kept  up  so  long  as  the  armature  revolves,  and 
a  continuous  current  of  electricity  is  obtained. 

The  object  of  the  commutator  and  brushes  is  to  make  sliding  con- 
tact with  the  armature,  which  revolves  at  a  high  speed,  and  also  to 
obtain  a  continuous  current  by  causing  the  coils  under  the  influence 
of  the  north  pole,  and  those  under  the  influence  of  the  south  pole  of 
the  field  magnet,  always  to  be  connected  with  the  circuit  in  the  same 
way,  and  therefore  to  produce  a  continuous  current. 

The  Siemens  Armature. — Another  important  form  of 
armature  is  the  Siemens  Drum  Armature,  which  consists  of 
a  drum  or  cylinder  of  iron  wound  longitudinally  with  a 


524    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

number  of  sections  of  insulated  copper  wire,  forming  one 
endless  coil.  Each  section  is  wound  in  a  different  direction 
or  plane,  and  is  connected  with  one  bar  of  the  commutator. 


FTG.  399.— WINDING  AN  ARMATURE. 

The  workmen  are  applying  the  insulated  copper  wire  lengthwise  around  the 
armature-core.  The  ends  of  the  section  in  which  the  wire  is  wound  are  seen  pro- 
jecting at  the  left.  These  ends  are  subsequently  attached  to  the  sections  of  the 
commutator  ;  and  insulated  binding-wire,  of  poorly  conducting  German  silver, 
is  wound  round  the  cylinder  in  successive  bands  to  hold  the  coils  in  place. 

The  action  of  this  armature  is  practically  the  same  as  that 
of  the  Gramme  ring ;  one  half  of  the  coils  generate  a  cur- 


ALTERNATING-CURRENT  DYNAMO.  525 

rent  in  one  direction  and  the  other  half  in  the  opposite 
direction,  the  two  currents  being  united  to  the  circuit  and 
taken  off  by  the  brushes.  The  Edison  dynamo-machine  has 
an  armature  of  the  Siemens  or  drum  type,  and  its  field 
magnet  is  a  massive  horseshoe. 

In  the  first  electrical  generators,  the  field  magnets  were  permanent 
magnets,  and  the  machines  were  called  magneto-electric  generators ; 
but  in  1867,  Siemens  and  Wheatstone  independently  conceived  the  idea 
of  using  the  current  generated  by  the  machine  itself  to  excite  the 
electro-magnets  which  formed  the  field  magnet.  This  great  invention 
was  thought  at  the  time  to  be  most  remarkable,  since  it  appeared  to 
imply  a  principle  similar  to  that  of  a  man  attempting  to  lift  himself 
by  his  own  boot-straps.  But,  as  a  matter  of  fact,  there  is  no  reason 
why  a  machine  should  not  feed  its  own  field  magnet,  since  the  current 
required  for  this  purpose  is  rarely  more  than  five  per  cent,  and  is  some- 
times as  low  as  one  per  cent,  of  the  total  current  produced  by  the  ma- 
chine. The  only  difficulty  is  that  there  must  be  some  magnetism  to 
start  with,  or  the  machine  will  not  "  excite  "  or  "  build  up."  There  is 
usually,  however,  sufficient  residual  magnetism  to  generate  a  little  cur- 
rent; this  strengthens  the  magnetism,  which  in  turn  produces  more 
current,  and  so  on,  till  the  full  strength  is  reached. 

The  Alternating-Current  Dynamo. — The  machines 
so  far  considered  produce  direct  currents — that  is,  currents 
which  always  flow  in  the  same  direction,  and  which  result 
from  the  use  of  the  commutator,  as  described.  If,  however, 
the  ends  of  the  coil  of  wire  forming  the  armature  are  con- 
nected with  two  copper  rings  on  the  shaft,  and  brushes  are 
kept  in  contact  with  these  rings  when  the  armature  revolves, 
then  an  alternating  current  will  be  produced,  because  the 
coil  will  first  pass  the  north  pole  and  then  the  south  pole, 
producing  a  current  first  in  one  direction,  then  in  the  other. 

This  kind  of  current  is  called  an  alternating  current,  and  its  im- 
portance and  extensive  use  are  due  to  the  fact  that,  by  means  of  a 
transformer,  which  is  merely  an  induction  coil,  the  E.  M.  F.  of  this  cur- 
rent may  be  raised  or  lowered  as  desired.  Hence,  it  is  possible  to  send 
a  current  of  high  E.  M.  F.  over  a  comparatively  small  wire,  and,  where 
it  enters  a  building,  to  reduce  the  E.  M.  F.  to  a  safe  point,  by  a  trans- 
former, thus  saving  the  cost  of  a  large  wire.  It  is  impossible  to  trans- 


526    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

form  a  continuous  current  in  this  way,  as  we  have  seen  that  a  steady 
current  has  no  inductive  effect.  An  alternating-current  dynamo,  capa- 
ble of  running  a  thousand  incandescent  lamps,  is  shown  on  page  505. 

Uses  of  Dynamos. — During  the  last  few  years,  thou- 
sands of  dynamos  have  been  built  and  put  in  use  for  a  great 


FIG.  400.— THE  EDISON  DYNAMO. 

many  different  purposes.  They  are  employed  to  generate 
electric  currents  for  electric  lighting,  electro-plating,  mo- 
tive power,  telegraphy,  charging  storage-batteries,  electric 
welding,  etc.  The  medical  electrical  machines,  which  turn 
by  a  handle,  are  virtually  small  dynamos. 

The  advantages  of  the  dynamo  are  twofold  :  First,  a  com- 
paratively small  machine  will  produce  a  powerful  current 
(for  instance,  a  machine  weighing  twelve  hundred  pounds 
— the  weight  of  a  large  horse — will  easily  generate  fifteen 
horse-power  of  electrical  energy) ;  secondly,  the  efficiency 
of  the  dynamo  is  remarkably  high,  there  being  machines  in 


ELECTRIC  MOTORS.  527 

practical  use  capable  of  generating  electric  power  to  the  ex- 
tent of  over  ninety  per  cent  of  the  mechanical  power  applied 
to  them.  The  mistake  should  not  be  made,  however,  of 
supposing  that  the  dynamo  runs  itself,  or  that  very  little 
power  will  run  it.  Mechanical  power  of  some  kind  must  be 
applied  to  the  shaft  in  order  to  turn  the  armature,  and  the 
result  obtained  in  electric  current  is  directly  proportional, 
and  nearly  equal,  to  the  mechanical  power  applied.  Only 
two  kinds  of  machines  are  commonly  used  for  running 
dynamos — the  steam-engine  and  the  water-wheel. 

Electric  Motors. — We  have  seen  that,  when  the  arma- 
ture of  the  dynamo  is  revolved,  a  current  is  generated ;  this 
action  can  be  reversed,  and  a  current  sent  through  the  arma- 
ture which  will  cause  it  to  revolve.  The  principle  here  is 
the  same  as  that  involved  in  the  production  of  a  current  in 
a  wire  moved  near  a  magnet,  and  conversely,  in  the  motion  of 
a  current-carrying  wire  near  a  magnet.  The  same  machine 
can  be  used  either  as  a  dynamo  or  a  motor,  a  good  dynamo 
being  a  good  motor ;  but  ordinarily,  for  practical  reasons, 
motors  are  made  slightly  different  from  dynamos. 

Electric  motors  are  used  for  many  purposes,  the  most  important 
of  the  applications  being  to  ventilating- fans,  pumps,  printing-presses, 
lathes,  drilling-machines,  circular  and  band  saws,  sewing-machines, 
grindstones,  etc.  The  great  advantages  of  electric  motors  are  that  they 
occupy  little  space,  they  require  little  or  no  skill  to  run  them,  arid 
they  are  economical,  for  the  reason  that  they  need  be  operated  only 
when  required,  as  the  current  can  be  turned  on  or  off  instantly. 

Transmission  of  Electrical  Energy. — The  dynamo  is 
a  machine  for  transforming  the  mechanical  energy  of  a 
steam-engine  or  water-wheel  into  electric  energy,  while  the 
electric  motor  transforms  the  energy  of  the  electric  current 
into  mechanical  energy.  It  is  obvious,  therefore,  that  we 
may  run  a  dynamo  with  a  steam-engine  or  water-wheel  at  a 
certain  place,  and  carry  the  current  produced  by  the  dynamo 
over  a  conducting  wire  to  an  electric  motor  at  some  other 
place  where  work  is  to  be  performed. 


528    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

The  transmission  of  energy  in  this  way  has  three  great  advan- 
tages :  First,  the  electricity  can  be  carried  a  great  distance  (even  as 
far  as  thirty  or  forty  miles) ;  second,  it  is  possible  to  run  a  great  many 
small  motors  for  different  purposes  from  one  circuit,  so  that  the  power 
generated  at  one  central  station  by  large  steam-engines  or  water- 
wheels  can  be  distributed  to  hundreds  of  different  motors  scattered 
through  a  manufacturing  town  ;  and  third,  the  electrical  energy  can 
be  transmitted  over  a  very  small  conductor,  a  wire  one  fourth  of  an 
inch  in  diameter  being  capable  of  transmitting  twenty-five  horse-power 
at  220  volts,  which  is  a  perfectly  safe  E.  M.  F. 

Electrical  Railways. — The  most  important  illustra- 
tion of  the  transmission  of  electrical  energy  is  the  electric 
railway.  The  commonest  and  most  successful  electric  rail- 
way system  consists  of  a  central  generating  station  having  a 
number  of  large  dynamos,  usually  run  by  steam-engines. 
From  this  station,  the  current  generated  is  carried  by  copper 
wires  along  the  line  of  the  railway,  usually  immediately  over 
the  middle  of  the  track  and  about  fifteen  feet  high.  The  cur- 
rent is  taken  off  this  conducting  wire  by  an  arm  attached  to 
the  top  of  the  car  and  having  a  trolley  at  the  end,  which  runs 
along  and  makes  continuous  contact  with  the  wire.  This 
current  is  carried  to  an  electric  motor  placed  underneath  the 
car  and  connected  with  the  axle.  When  the  man  running 
the  car  wishes  to  move  forward,  he  simply  closes  the  circuit 
with  a  switch  and  allows  the  current  to  flow  through  the 
motor,  thus  causing  the  motor  and  car-wheels  to  revolve. 
In  order  to  cause  the  car  to  move  backward,  the  current 
through  the  motor  is  reversed. 

Instead  of  running  street-cars  by  this  overhead-wire  system,  stor- 
age-batteries placed  directly  upon  the  car  itself  are  sometimes  em- 
ployed to  furnish  the  current  for  the  motor.  This  plan  has  an  advan- 
tage in  that  the  car  carries  its  own  supply  of  electricity,  and  therefore 
requires  no  wire  leading  along  the  track.  The  disadvantage  of  the 
system  is  the  great  weight  of  the  batteries,  which  amounts  to  several 
thousand  pounds.  The  storage-battery  used  for  this  purpose  will  be 
described  later  (see  page  535). 


HEATING  AND  LIGHTING  EFFECTS.  529 

QUESTIONS.— Illustrate  Electro-magnetic  Induction.  How  is  the  phenomenon  ex- 
plained ?  Can  you  suggest  an  experiment  which  will  throw  further  light  upon 
the  principle  ?  Show  how  electro-magnetic  inductive  action  is  applied.  Ex- 
plain the  construction  of  the  Induction  Coil.  State  fully  the  principle  in- 
volved. Give  an  idea  of  the  power  and  uses  of  the  induced  current.  What  is 
gained  by  this  transformation  of  electricity  ? 

What  purpose  does  the  Telephone  serve  ?  Explain  the  principle  of  the  ordinary 
Bell  Telephone  ;  illustrate  by  diagram.  Of  what  does  the  usual  form  of  trans- 
mitting telephone  consist  ?  Draw  a  diagram  illustrating  the  details  of  a  tele- 
phone circuit.  Describe  the  Microphone. 

State  the  importance  of  the  Dynamo-Electric  Machine,  and  the  principle  of  its 
construction.  Upon  what  does  the  power  of  the  current  obtained  by  means  of 
this  machine  depend  ?  What  is  essentially  the  common  dynamo  ?  Describe 
the  Gramme  ring  ;  the  Siemens  armature.  How  is  the  current  generated  by 
the  machine  itself  utilized  to  excite  the  electro-magnets  ?  Describe  the  Alter- 
nating-Current Dynamo,  and  state  its  advantages.  What  are  the  uses  of 
dynamos  ?  What  kind  of  machines  are  employed  for  running  them  ?  Explain 
the  principle  of  Electric  Motors.  For  what  are  they  used,  and  what  are  their 
advantages  ?  How  is  electrical  energy  transmitted  ?  Describe  two  methods  of 
running  street-cars  by  electricity. 


HEATING  AND  LIGHTING   EFFECTS   OF 
ELECTRICITY. 

Production  and  Control  of  Heating  Effect If  a 

strong  current  of  electricity  is  passed  through  a  small  wire, 
the  wire  will  become  heated ;  if  the  strength  of  the  current 
be  increased,  its  temperature  will  rise  until  it  becomes  red- 
hot,  then  white-hot,  and  finally  the  wire  may  even  melt  or 
vaporize.  It  is  difficult  to  get  great  heating  effects  from  a 
small  number  of  cells ;  but  two  or  three  cells  of  a  bichro- 
mate of  potash  battery,  particularly  if  connected  in  parallel, 
will  give  a  sufficient  current  to  heat  a  fine  copper  wire  or 
an  iron  wire  red-hot.  The  thinner  the  wire  and  the  shorter 
its  length,  the  easier  it  is  heated.  The  principles  and  quan- 
titative facts  in  regard  to  the  heating  effects  of  currents 
have  been  fully  described  on  page  500. 

The  currents  from  dynamo-machines  are  strong  enough  to  melt 
wire,  although  it  is  dangerous  to  use  them  for  this  purpose,  as  it  puts 
a  sudden  strain  upon  the  machine  and  is  also  liable  to  melt  the  wires 
with  which  the  armature  is  wound.  Large  dynamo-machines  have 
been  made  capable  of  giving  a  current  strong  enough  to  melt  a  solid 
bar  of  copper  as  thick  as  a  man's  wrist. 


530     PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

The  most  important  application  of  this  heating  effect  is 
the  electric  lamp,  which  is  merely  a  device  for  producing 
it  with  sufficient  intensity  and  steadiness  to  give  a  practical 
light.  There  are  two  kinds  of  electric  lamps,  the  arc  and 
the  incandescent  or  glow  lamp. 

Arc  Lamps. — If  the  terminals  of  two  wires  leading 
from  a  powerful  battery  or  dynamo  be  brought  together, 
and  then  separated  about  an  eighth  or  sixteenth  of  an  inch, 
the  current  will  continue  to  flow  across  the  space  between 

the  ends  of  the  wires,  producing 
a  light  of  dazzling  brilliancy. 
This  light  is  due  to  the  intense 
heating  effect  of  the  current 
caused  by  the  resistance  at  the 
point  where  it  flows  across.  The 
ends  of  the  wires  are  raised  to 
a  white-heat  of  sufficient  inten- 
sity to  melt  any  known  sub- 
stance, including  even  platinum 
and  the  diamond. 

As  terminals  made  ot  metal  rap- 
idly melt,  pencils  of  carbon,  which 

FIG.  401.— THE  ELECTRIC  ARC.        is  the  most  infusible  of   substances, 

are  used  for  this  purpose.  Two  car- 
bon rods  with  the  current  passing  between  them  are  shown  in  Fig. 
401.  It  will  be  noticed  that  the  path  of  the  current  is  in  the  form  of 
an  arc,  from  which  fact  the  arc  lamp  and  voltaic  arc  take  their  names. 
Even  carbon  is  slowly  vaporized  and  burned  away  in  the  electric  arc ; 
therefore,  to  make  the  light  steady,  it  is  necessary  to  have  some  way  of 
feeding  the  carbons  as  they  burn.  This  is  accomplished  by  clock- 
work mechanism,  which  feeds  the  carbons  together  as  fast  as  they  are 
consumed ;  or  by  means  of  a  mechanical  clutch  arrangement,  which 
allows  the  upper  carbon  to  drop  a  little  by  its  own  weight  when  the 
distance  between  the  carbons  becomes  too  great.  A  regular  form  of 
arc  lamp  is  shown  in  Fig.  402. 

The  Incandescent  Lamp  consists  of  a  thin  conductor, 
which  is  made  nearly  white-hot  by  the  current.  Platinum 


ELECTRIC  LIGHTING. 


531 


wire  was  first  used  for  this  purpose,  but 
it  was  found  liable  to  melt ;  thin  strips 
or  filaments  of  carbon  were  therefore 
substituted  in  incandescent  lamps. 

The  filament  of  the  Edison  lamp  is 
carbonized  bamboo;  but  carbonized 
thread  and  even  hair  have  been  em- 
ployed for  this  purpose.  The  use  of 
carbon  makes  it  absolutely  necessary  to 
remove  all  the  air  from  around  the  fila- 
ment, otherwise  it  would  be  burned  up 
as  soon  as  it  became  red-hot.  Hence, 
the  filaments  are  inclosed  in  a  glass 
bulb,  from  which  the  air  is  pumped  with 
a  mercury  air-pump ;  the  bulb  is  then 
hermetically  sealed.  The  air-pump 
used  is  so  effective  that  only  one-mill- 
ionth part  of  the  air  is  left  in  the  bulb. 

The  construction  of  the  Edison  lamp  is 
shown  in  Fig.  403,  in  which  G  is  the  glass 
bulb,  L  is  the  loop  or  filament  of  carbon,  E  E 
are  platinum  wires  connected  with  the  ends 
of  the  filaments  and  leading  through  the  glass, 
one  of  which  is  connected  with  the  brass  ring, 
B,  and  the  other  with  the  brass  button,  D,  at 
the  bottom  of  the  lamp.  When  the  lamp  is 
screwed  into  the  socket  that  holds  it,  this 
ring  and  button  are  in  contact  with  brass 
pieces  in  the  socket,  which  in  turn  are  con- 
nected with  the  wires  supplying  the  current. 

An  electric  lighting  plant  consists  of  one 
or  more  dynamos  for  generating  the  current, 
switches  for  controlling  the  current,  wires  for 
carrying  the  current  to  the  places  where  it  is 
to  be  used,  and  lamps  for  converting  the  cur- 
rent into  light. 

The  two  kinds  of  lamps  are  connected 
with  the  circuit  in  entirely  different  ways. 
Arc  lamps  are  connected  in  series — that  is, 


FIG.  402.— THE  ARC  LAMP. 


FIG.  403.— EDISON  INCAN- 
DESCENT LAMP. 


532    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

the  current  flows  through  one,  then  the  next,  and  so  on — whereas  the 
incandescent  lamps  are  connected  in  parallel — that  is,  the  current 
divides  or  branches  into  a  number  of  parts,  each  of  which  flows  through 
a  single  lamp.  The  chief  advantage  of  arc  lamps  is  their  great  power 
and  comparative  economy  of  current.  Thus  it  costs  only  two  or  three 
cents  an  hour  to  produce  a  light  of  six  or  eight  hundred  candle-power ; 
and  only  a  single  small  wire  is  required,  which  may  be  run  for  six  or 
eight  miles,  with  the  lamps  attached  wherever  desired.  Arc  lighting 
is  suited  to  large  spaces,  such  as  streets  and  parks.  The  advantages 
of  incandescent  lighting  are  that  the  light  is  more  distributed  and  not 
so  intense  at  one  point,  and  that  it  is  very  much  more  steady  than  the 
arc  light— in  fact,  it  is  among  the  steadiest  artificial  lights  known. 

The  electric  light  has  been  used  in  capturing  deep-sea  fishes  two 
miles  below  the  surface ;  it  is  proposed  to  employ  it  in  photographic 
apparatus  for  the  purpose  of  making  negatives  of  the  ocean-bottom. 

Danger  in  Electric  Lighting. — Arc  lamps,  being 
almost  always  run  in  series,  require  a  high  E.  M.  F.,  usually 
from  1,000  to  3,000  volts.  Incandescent  lamps,  on  the  other 
hand,  being  almost  always  run  in  parallel,  require  only  from 
50  to  120  volts.  The  principle  of  this  difference  has  been 
illustrated  by  pumps  on  page  478.  It  therefore  follows  that 
touching  an  arc  circuit  is  usually  much  more  dangerous 
than  contact  with  an  incandescent  circuit,  the  effect  on  any 
animal  being  directly  proportional  to  the  E.  M.  F.,  other 
things  being  equal.  The  danger  limit  is  between  300  and 
500  volts ;  below  this  the  effect  may  be  disagreeable,  but  is 
not  serious.  All  danger  is  obviated  by  perfect  insulation 
and  avoidance  of  actual  contact. 

Electric  Welding. — There  are  other  applications  of 
the  heating  effect  of  electricity  besides  electric  lighting. 
The  most  important  and  most  recently  developed  of  these 
is  electric  welding.  The  art  consists  simply  in  placing  to- 
gether the  two  pieces  of  metal  to  be  welded,  and  passing  a 
very  powerful  electric  current  through  the  juncture.  This 
heats  the  surfaces  of  the  metal  in  contact  to  such  an  extent 
that  they  fuse  together  and  make  a  perfectly  solid  joint. 
The  convenience  and  effectiveness  of  electric  welding  are 


ELECTRIC   WELDING  AND  PLATING.  533 

remarkable.  Only  the  surfaces  of  the  two  metals  are  heated ; 
therefore  the  amount  of  heat  required  is  very  small,  and 
the  metals  are  not  made  black  and  dirty  as  they  would  be  if 
placed  in  a  fire.  It  is  also  possible  in  this  way  to  weld 
brass  and  copper  to  iron  and  steel.  Heretofore,  welding 
had  been  confined  to  iron  and  steel ;  new  it  is  possible  to 
weld  electrically  almost  any  two  metals. 

The  ordinary  form  of  electric  welding  apparatus  consists  of  two 
sliding  clamps  for  holding  the  metals  to  be  welded.  These  are  con- 
nected with  a  dynamo-machine  specially  made  to  give  a  current  of 
several  thousand  amperes.  When  the  metals  are  brought  in  contact, 
the  current  flows  across  the  joint  and  fuses  them  together.  The  cur- 
rent is  then  stopped  and  the  joint  solidifies. 

Electric  Furnaces. — Electricity  has  been  used  in  a 
somewhat  similar  manner  for  reducing  metallic  ores,  melt- 
ing metals,  etc.  The  electric  furnace  or  crucible  for  this 
purpose  is  provided  with  two  electrodes  or  conductors,  usu- 
ally heavy  plates  of  carbon,  between  which  the  material  to 
be  treated  is  placed.  When  a  powerful  current  is  passed 
between  the  electrodes,  the  material  is  intensely  heated. 

Electricity  lias  even  been  used  for  Cooking  Pur- 
poses, the  heat  being  produced  by  passing  a  strong  current 
through  conductors  which  offer  resistance  to  its  passage. 
For  example,  if  a  coil  of  wire  be  placed  in  a  vessel  of  water, 
and  a  strong  current  be  passed  through  it,  the  water  will 
become  sufficiently  heated  to  boil  an  egg. 


CHEMICAL  EFFECTS  OF  ELECTRICITY. 

Electro-Plating-. — When  an  electric  current  is  passed 
through  any  liquid  which  is  a  conductor,  a  chemical  effect 
is  usually  produced  in  the  liquid.  In  the  case  of  a  solution 
of  some  metal,  the  latter  will  be  deposited  on  the  cathode, 
as  already  described  (page  488). 

The  article  to  be  plated  is  connected  with  the  negative  pole  of  the 
battery  or  dynamo,  and  a  piece  of  the  metal  for  plating  is  connected 


534    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

with  the  positive  pole.    This  arrangement  is  shown  in  Fig.  404,  where 
A  is  a  silver  anode  connected  with  the  positive  wire,  and  C  is  a  spoon 

to  be  plated,  connected 
with  the  negative  wire. 
A  resistance  switch,  S,  is 
inserted  into  the  circuit 
to  regulate  the  strength 
of  the  current.  The  anode 
and  cathode  are  hung  in 
a  bath  consisting  of  a 
solution  of  silver,  and  as 
soon  as  the  current  is 
caused  to  pass  between 
the  anode  and  the  spoon, 
the  solution  will  be  de- 


FIG.  404.— ELECTKO-PLATING  APPARATUS. 


composed  and  the  silver  will  be  deposited  on  the  spoon,  the  thickness 
of  the  coating  depending  upon  the  strength  of  the  current  and  the 
length  of  time  it  passes. 

Secondary,  or  Storage-Batteries. — The  principle  of 
Storage-Batteries  is  very  similar  to  that  of  electro-plating. 
The  batteries  are  made  up  of  plates  of  lead  (the  electrodes), 
or  an  alloy  of  lead,  cast  in  the  form  of  a  "  grid/'  or  frame- 


STORAGE  BATTERIES. 


535 


i 


work  of  bars  crossing  one  another  at  right  angles,  as  snown 
in  Fig.  405.  The  holes  in  the  plate  are  filled  with  a  paste 
of  lead  oxide.  For  the  positive  plates,  the  paste  is 
made  of  red  lead  and  sulphuric  acid ;  while  for  the 
negative  plates,  litharge  and  sulphuric  acid  are  used. 
The  positive  and  negative  plates  are  placed  al- 
ternately in  a  bundle  (Fig.  406).  They  are  kept 
apart  by  strips 
of  rubber  and 
bound  by  strips 
of  wood  dove- 
tailed together. 
The  plates  are 
supported  on 
wooden  blocks, 
which  in  turn 
rest  upon  the 
bottom  of  the 
glass  jar.  The 
negative  plates 
of  one  cell  are 
all  connected  in 
parallel  at  one 
end  of  the  cell 

by  means  of  their  connecting  strips.  The  positive  plates 
are  connected  at  the  other  end.  The  manner  of  connecting 
the  cells  is  shown  in  Fig.  407.  The  liquid  surrounding  the 
plates  is  dilute  sulphuric  acid. 

When  the  battery  has  been  exhausted,  it  is  charged  by  connecting 
a  dynamo  with  the  terminals  of  the  battery,  and  sending  a  current 
through  it.  This  current  reverses  the  chemical  action,  which  goes  on 
during  the  discharge  of  the  battery.  As  already  stated,  the  plating- 
vat  behaves  in  a  similar  manner. 

Storage-batteries  have  an  electro-motive  force  of  2*2  volts  per  cell. 
The  resistance  per  cell  depends  on  the  size  and  number  of  plates  com- 
posing each  cell ;  it  is  usually  0-005  ohm,  or  less. 


Fia.  405. — STORAGE- BATTERY  :  THE  GRID. 


536    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 


The  main  difficulties  with  such  cells  are  that  the  paste  drops  out 
of  the  holes  in  the  lead  plates,  and  the  plates  finally  warp  or  buckle 
and  come  in  con- 
tact with  one  an- 
other within  the 
liquid,  thus  mak- 
ing a  short  cir- 
cuit which    dis- 
charges the  cell. 

What  is  effected  in 
the  storage-battery  is  the 
electrical  storage  of  en- 
ergy, not  the  storage 
of  electricity.  Properly 
speaking,  the  energy  is 
put  into  the  form  of 
chemical  affinity,  and 
there  is  really  no  more 
electricity  in  the  cell 
when  it  is  charged  than 
after  it  is  discharged. 
The  storage-battery  is  a 
very  convenient  means 
of  taking  electrical  en- 
ergy at  one  time  or  place 
and  using  it  at  some 
other  time  or  place.  An 
idea  of  the  amount  of 
storage-battery  required 
for  any  given  purpose 
may  be  obtained  from 
the  statement  that  a  bat- 
tery capable  of  giving  one 
horse-power  for  five  hours 
weighs  500  pounds,  or,  in 
other  words,  it  will  sup- 
ply twelve  incandescent 
lamps  of  sixteen  candle- 
power  each  for  five  hours; 
but  then  it  will  have  to 
be  recharged  by  the  cur- 
rent from  a  dynamo.  FIG.  407.— METHOD  OF  CONNECTING  CELLS, 


FIG.  406.— ARRANGEMENT  OF  POSITIVE  AND 
NEGATIVE  PLATES. 


MILITARY  APPLICATIONS  OP  ELECTRICITY.      537 


ELECTRICITY  IN  WARFARE. 

Electricity  011  Ships-of-War. — One  of  the  most  im- 
portant and  extensive  applications  of  electricity  is  to  military 
and  naval  operations.  The  electric  search-light,  which  is 
merely  a  very  powerful  arc  lamp  with  a  reflector,  may  be 
effectively  used  on  a  ship-of-war  at  night  to  enable  her  to 


FIG.  408.— SHIP-OF-WAR  USING  HER  SEARCH-LIGHTS. 

enter  harbors,  avoid  obstructions,  detect  the  presence  of  los- 
tile  vessels,  torpedo-boats,  floating  torpedoes,  etc.  A  i  im- 
ber  of  electric  motors  are  often  employed  on  a  mari-of  war 
to  drive  ventilating-fans,  manipulate  the  heavy  guns,  '  oist 
and  set  in  place  the  enormous  cartridges,  revolve  the  tur- 
rets, etc.  Electric  signals  also  place  in  communication  dif- 
ferent parts  of  the  vessel. 
35 


538    PRACTICAL  APPLICATIONS  OF  ELECTRICITY. 

Electricity  has  been  employed  in  land  warfare  for  field 
telegraphing,  exploding  mines  and  torpedoes,  illuminating 
magazines,  where  the  use  of  any  other  artificial  light  would 
be  perilous,  etc.  The  velocity  of  cannon-balls  is  now  accu- 
rately measured  through  the  agency  of  electricity. 

ELECTRICITY  IN  MEDICINE  AND  SURGERY. 
The  Uses  of  Electricity  in  Medical  Practice   are 

many  and  varied.  Applied  to  the  muscles  or  nerves,  it  may 
tell  us  of  the  presence  of  disorder ;  and,  where  derangement 
is  found  to  exist,  it  may  restore  the  functions  of  the  organs 
involved,  as  in  cases  of  curable  paralysis  and  wasting  of  the 
muscles.  The  sudden  change  of  state  produced  in  the  mus- 
cle or  nerve  by  the  interrupted  current,  throws  it  into  healthy 
action.  In  disorders  of  the  brain  and  spinal  cord,  the  use 
of  electricity  is  often  followed  by  favorable  results ;  while  in 
certain  forms  of  neuralgic  troubles,  like  lumbago  and  sciat- 
ica, it  sometimes  affords  speedy  and  permanent  relief.  In 
conditions  attended  with  failure  in  respiration,  as  in  poison- 
ing by  opium  or  impending  heart-failure,  life  may  be  saved 
by  exciting  the  muscles  of  breathing  with  a  Faradic  cur- 
rent. There  are  also  conditions  in  which  electricity  has  a 
general  tonic  effect  on  the  whole  system. 

Physicians  employ  the  electric  light  for  illuminating  the  cavities 
of  the  ear,  nose,  mouth,  throat,  and  stomach.  Objects  that  could  not 
otherwise  be  seen  and  investigated  are  thus  brought  into  view. 

A  platinum  wire  heated  to  a  white-heat  by  the  galvanic  current 
forms  an  instrument  known  as  the  galvano-cautery,  of  great  service 
.in  the  hands  of  the  surgeon  for  the  removal  of  tumors  and  diseased 
tissues.  Electric  engines  are  used  both  by  surgeons  and  dentists  to 
furnish  the  steady  power  necessary  for  the  manipulation  of  instru- 
ments in  delicate  operations. 

In  order  that  benefit  may  be  derived  from  electrical 
treatment,  it  must  be  applied  by  an  experienced  and  care- 
ful practitioner.  In  the  hands  of  the  charlatan,  electricity 
is  an  uncertain  and  even  dangerous  agent, 


QUESTIONS  AND   PROBLEMS.  539 

QUESTIONS.— What  can  you  say  of  the  production  and  control  of  Electrical  Heat- 
ing Effect  ?  Explain  the  principle  of  the  Arc  Lamp.  Why  are  carbons  used, 
and  how  is  the  feeding  of  the  carbons  regulated  ?  Describe  the  Incandescent 
Lamp,  and  illustrate  the  principle  by  diagram.  Of  what  does  an  electric 
lighting  plant  consist  ?  State  the  advantages  of  arc  lamps  ;  of  incandescent 
lighting.  Discuss  the  question  of  danger  in  connection  with  each. 

Describe  Electric  Welding,  and  show  what  has  been  accomplished  in  this  line. 
How  has  electricity  been  utilized  for  smelting  and  cooking  purposes  ?  Describe 
the  process  of  Electro-plating.  Explain  the  Storage-battery  and  its  applica- 
tions. What  are  the  objections  to  Storage-batteries.  State  the  uses  of  elec- 
tricity in  warfare  ;  in  medicine  and  surgery. 

MISCELLANEOUS  QUESTIONS  AND  PROBLEMS. 

Assume  that  you  have  a  lathe  in  your  workshop,  and  half  a  mile  away  there  is  a 
small  waterfall  ;  describe  a  means  of  driving  your  lathe  by  this  water-power. 
(Suggestions :  Water-wheel,  small  dynamo,  wire  to  workshop,  electric  motor 
belted  to  lathe.)  The  earth  can  be  used  as  the  return  conductor  by  burying  a 
plate  at  each  end  of  the  line. 

If  a  ten-horse-power  water-wheel  is  used  to  drive  a  dynamo,  the  current  from 
which  runs  an  electric  motor  half  a  mile  away,  what  is  about  the  maximum 
power  that  can  be  obtained  from  the  motor  ?  About  seven  horse-power  ;  be- 
cause one  horse-power  would  be  lost  in  the  dynamo,  one  on  the  line  wire,  and 
one  in  the  motor,  these  losses  being  due  to  friction,  heating  of  the  wire,  etc. 

Foucault  revolved  a  copper  disk  between  the  poles  of  a  strong  magnet,  and 
found  a  decided  resistance  to  the  revolution  of  the  disk,  although  it  did  not 
touch  the  poles ;  the  disk  also  became  hot.  Why  ?  And  why  would  such  a 
disk  become  hotter  than  the  armature  of  a  dynamo  which  also  revolves  be- 
tween the  poles  of  a  strong  magnet  ?  TJie  disk  had  currents  generated  in  it 
exactly  as  in  the  armature  of  a  dynamo,  only  in  FoucauWs  disk  the  currents 
flowed  round  and  round,  thereby  heating  the  disk  ;  ivhereas  in  the  armature 
of  a  dynamo  the  wires  are  separated  by  being  insulated,  which  prevents  these 
local  currents  between  the  different  parts  of  the  coil.  But  if  two  parts  of  a  coil 
cut  through  the  insulation  and  come  in  metallic  contact,  causing  a  "short 
circuit,"  then  that  portion  of  the  coil  becomes  very  hot,  like  Foucault's  disk. 

If  you  wind  an  ordinary  horseshoe  permanent  magnet  with  a  number  of  turns  of 
wire,  the  ends  of  which  are  connected  with  a  galvanometer,  and  then  alternately 
put  on  and  pull  off  the  keeper  of  the  magnet,  what  effect  will  be  produced  in 
the  galvanometer  ?  The  needle  will  swing  one  way  when  the  keeper  is  put  on, 
and  the  other  way  when  it  is  taken  off,  because  of  the  generation  of  currents 
by  the  increase  in  the  number  of  lines  of  magnetic  force  passing  through  the 
coil  in  the  first  case,  and  the  decrease  of  lines  of  force  in  the  second  case.  This 
action  is  precisely  like  that  of  the  Bell  telephone  when  used  as  a  transmitter. 

What  effect  is  produced  on  the  light  given  by  an  incandescent  lamp  when  the 
electro-motive  force  supplied  to  it  is  raised  ?  If  there  is  a  great  increase  in 
light,  why  not  always  run  incandescent  lamps  at  a  high  electro-motive  force  ? 
TJie  light  increases  very  rapidly  by  increase  of  E.  M.  F.,  being  doubled  with 
only  about  ten  per  cent  increase  in  electrical  energy.  Unfortunately,  the  life 
of  the  lamp— i.  e.,  the  average  number  of  hours  it  will  burn  without  renewal- 
is  greatly  reduced  when  it  is  run  at  a  high  temperature,  because  of  the  deteri- 
oration of  the  filament ;  therefore  a  compromise  is  adopted,  the  proper  point 
being  that  at  which  the  lamp  gives  a  yellowish  and  not  a  Wm's/i-white  light. 


540    TABLE  OF  ENGLISH  AND  METRIC  MEASURES. 


COMPARATIVE   TABLE  OF  ENGLISH  AND  METRIC 
MEASURES. 

MEASURES   OF   LENGTH. 
Standard  unit,  one  metre. 

1  kilometre    =  1,000  metres.  1  decimetre   =  O'lOO  metre. 

1  hectometre=    100       "  1  centimetre  =  O'OIO 

1  decametre  =      10  1  millimetre  =  O'OOl       " 


1  metre          =  39'37079  inches.  1  inch  =  2'53995    centimetres. 

1  decimetre  =   3'93708       "  1  foot  =  3'04794   decimetres. 

1  centimetre  =   0-39371       "  1  yard  =  0-914383  metre. 

1  millimetre  =   0-03937      "  1  imV=  1-609315  kilometres. 

To  reduce  kilometres  to  miles,  multiply  by  -62138. 

MEASURES   OF   SURFACE. 

1  sq.  metre          =  107643  sq.  feet.  1  sq.  foot  =  9'28997  sq.  dm, 

1  sq.  centimetre  =   0'1550  sq.  inch.  1  sq.  inch  =  6-45137  sq.  cm. 

1  sq.  millimetre  =   0'0015  sq.  inch.  1  sq.  yard  =  0-8361  sq.  m. 

To  reduce  kilom-carres  (square  kilometres)  to  square  miles,  multiply  by 
•386116. 

MEASURES   OF   VOLUME. 

1  litre  =        1  cubic  decimetre. 

1    "    =  1,000     u      centimetres. 

1  litre     =  61-02705  cu.  inches.  1  cu.  inch  =  16'38618  cu.  cm. 

1  cu.  cm.  =   0-06103  cu.  inch.  1  cu.  foot  =  28'31531  cu.  dm, 

1  litre     =   1-05672  U.  S.  qts.  1  U.  S.  qt.  =     0'946&itre. 

MEASURES   OF  WEIGHT. 

The  unit,  one  gramme,  is  the  weight  of  one  cubic  centimetre  of  distilled 
water,  at  the  temperature  of  4°  C. 

1  kilogramme    =  1,000  grs.  1  decigramme  =  O'lOOO  gr. 

1  hectogramme  =     100   "  1  centigramme  =  O'OIOO   " 

1  decagramme  =      10   "  1  milligramme  =  O'OOIO   " 


1  kilogr.  =   2-204621  Ib.  avoir.  1  grain        =  64799     milligr. 

1      "      =32-15073   oz.  troy.  1  oz.  troy    =31 '1035   gr. 

1  gr.        =  15-43235    grains.  1  Ib.  avoir.  =   0'45359  kilogr. 

One  thousand  kilogrammes  varies  but  little  from  the  "  long  "  ton  of  2,240 
pounds  avoirdupois  (0'984206  ton). 

The  pound  avoirdupois  contains  7,000  grains. 

The  same  figures  which  represent  the  specific  gravity  of  any  solid  or  liquid, 
referred  to  water  as  unity,  also  represent  the  weight  of  one  cubic  centimetre  of 
the  substance,  expressed  in  grammes. 


INDEX. 


Absorption,  210. 

Acceleration,  19. 

Acoustics,  370. 

Adhesion,  167  ;  of  liquids,  173. 

Air  (see  Atmosphere). 

Air-dome,  the,  217. 

Air-pump,  the,  211,  212. 

Alloys,  248. 

Ampere,  the,  488. 

Ampere-meter,  the,  491. 

Ampere's  Rule,  491. 

Aneroid  barometer,  204. 

Angle  of  repose,  155. 

Animal  heat,  273. 

Annealing,  176. 

Astigmatism,  349.  f 

Atmosphere,   the,   222-227 ;    depth    of, 

224;  pressure  of,  225;  buoyancy  of,  225. 
Atmospheric  humidity,  260. 
Atomic  theory,  70. 
Atoms,  Thomson's  theory  of,  68,  69  ;  as 

distinguished    from    molecules,    71  ; 

spaces  between,  72  ;  size  of,  74,  75. 
Audiphones,  388. 
Aurora,  the,  465. 

Balance,  the  equal-arm,  163. 

Balance-wheel,  the,  137. 

Balloon,  the,  226. 

Barometer,  the,  202-204 ;  aneroid,  204, 

205  ;  heights  measured  by,  225. 
Batteries,  460  ;  arrangement  of  cells  in, 

476  ;  analogy  between  the  action  of, 

and  pumps,  478  ;  storage,  534-536. 
Boiling,  phenomena  of,  250  ;  below  100° 

C.,  255. 

Boiling-points,  251. 
British  engineering  units,  98-100. 

Calorimeter,  the,  246 ;  for  measuring 
heat  in  current-carrying  wire,  501 . 

Camera  lucida,  the,  "  317  ;  photogra- 
pher's, 344. 


Capillarity,  177,  178. 

Cause  and  effect,  3. 

Center  of  gravity,  mass,  or  weight,  126  ; 
method  of  finding,  127. 

Centrifugal  tendency,  111-117. 

Chance,  4. 

Chromatic  aberration,  330,  351. 

Cohesion,  167  ;  of  liquids,  173. 

Collision,  as  a  source  of  heat,  270. 

Color,  328  ;  of  bodies,  334,  335. 

Color-blindness,  336. 

Color  fatigue,  336. 

Colors,  combination  of,  330,  333  ;  com- 
plementary, 332  ;  mutual  effect  of, 
337. 

Color-sense,  336. 

Combustion,  271,  272. 

Compressibility,  50  ;  of  gases,  205  ;  law 
of,  206. 

Compression,  a  source  of  heat,  275. 

Conduction,  of  heat,  276  ;  of  electricity, 
438. 

Convection,  279. 

Couples,  113. 

Critical  angle,  316. 

Density,  11,  195. 

Dew-point,  the,  261. 

Diffusion,     179-181  ;     of     gases,    220  ; 

through   membranes,  222 ;    of  heat, 

276. 

Dip-batteries,  475. 
Direction,  13. 
Discord,  416. 
Distillation,  252,  253. 
Divisibility,  67,  68. 
Ductility,  169. 

Dynamo,  alternating-current,  the,  525. 
Dynamo-electric  machine,  the,  522. 

Ear,  the,  371. 

Ear- trumpets,  388. 

Earth,  the,  tendency  of,  to  approach  a 


542 


INDEX. 


body,  54 ;  magnetism  of,  430 ;  mag- 
netic pole  of,  431. 

Echoes,  387. 

Elasticity,  49,  170 ;  of  stretch,  49 ;  of 
compression,  50 ;  of  bending,  51 ;  of 
torsion,  51. 

Electricarattraction  and  repulsion,  53, 
437,440. 

Electrical  machines,  446-453. 

Electrical  railways,  528. 

Electrical  resistance,  480. 

Electric  bells,  515. 

Electric  clocks,  515. 

Electric  current,  the,  468 ;  measure- 
ment of,  488  ;  heating  effect  of,  500. 

Electricity,  435-540  ;  phenomena  of, 
436 ;  voltaic,  469 ;  applications  of, 
505  ;  in  warfare,  537 ;  in  medicine, 
538. 

Electric  lamps,  529-532. 

Electric  motors,  527. 

Electric  spark,  effects  of,  461. 

Electric  welding,  532. 

Electrodes,  489. 

Electro-magnet,  the,  506. 

Electrometers,  494. 

Electro-motive  force,  493  ;  of  cells,  497. 

Electrophorus,  the,  445. 

Electro-plating,  533. 

Electroscope,  the,  441. 

Elements,  the  chemical,  10. 

Energy,  28^3  ;  compared  with  work, 
28 ;  nature  of,  31 ;  increase  of,  with 
velocity,  32 ;  forms  of,  34-39  ;  of  on- 
ward motion,  35  ;  of  visible  vibration, 
35  ;  of  sound  vibration,  36  ;  of  heat, 
37  ;  radiant,  38  ;  conservation  of,  39, 
40 ;  transformation  of,  40 ;  availa- 
bility of,  41 ;  potential,  42,  97  ;  chemi- 
cal, 70  ;  measurement  of,  94,  95  ;  of 
rotation,  95  ;  unit  of,  95. 

Equilibrium,  of  moments,  112 ;  of  bodies, 
in  respect  to  weight,  126  ;  stable  and 
unstable,  128  ;  neutral,  129. 

Evaporation,  phenomena  of,  250. 

Expansion,  of  gases,  208,  243  ;  of  solids, 
by  heat,  233;  of  liquids  and  gases,  by 
heat,  234 ;  law  of,  237 ;  coefficient  of 
linear,  237  ;  coefficient  of  cubical,  240  ; 
of  water,  241. 

Extension,  61,  62. 

Eye,  the,  346  ;  care  of,  352. 


Falling  bodies,  121,  122. 

Faults,  on  telegraph  lines,  486,  511. 

Floating  bodies,  194. 

Foci,  of  mirrors,  305-308 ;  of  lenses, 
322-325  ;  real  and  virtual,  323. 

Force,  definition  of,  43,  44  ;  action  of, 
44,  45  ;  recognition  of,  45,  46  ;  exam- 
ples of,  49-54  ;  changing  direction  of 
motion,  55  ;  production  of,  by  energy, 
56  ;  unit  of,  70  ;  moment  of,  111  ;  cen- 
tral, 113. 

Forces,  balanced,  47,  48  ;  examples  of, 
49-54  ;  measurement  of,  82,  84,  85,  91 ; 
action  of,  105  ;  composition  of,  105 ; 
equilibrium  of,  106 ;  resolution  of, 
107,  109. 

Freezing,  phenomena  of,  242. 

French  engineering  units,  100. 

Friction,  138 ;  laws  of,  139  ;  of  repose, 
140 ;  of  gases  and  liquids,  141  ;  a 
source  of  heat,  268. 

Fusion,  247  ;  laws  of,  249. 

Galvanometer,  the,  467,  499. 

Gases,  166  ;  properties  of,  200-228  ;  com- 
pressibility of,  205  ;  expansion  of, 
208  ;  absorption  of,  210  ;  diffusion  of, 
220. 

Gramme  ring,  the,  523. 

Gravitation,  119-132 ;  not  affected  by 
interposing  body,  120. 

Gravity  cell,  the,  473. 

Grove  cell,  the,  474. 

Hardness,  169. 

Harmonics,  the,  of  a  vibrating  string, 

391,392. 
Harmony,  416. 
Hearing,  mechanism  of,  371. 
Heat,  230-292 ;  a  form  of  energy,  37, 

230  ;  effects  of,  232  ;  quantity  of,  245  ; 

specific,  246  ;  sources  of,  267  ;  animal, 

273  ;  diffusion  of,  276. 
Heat-engines,  285. 
Heat- waste  in  wires,  502. 
Horse-power,  the,  101. 
Humidity,  atmospheric,  260  ;  relative, 

262. 

Hydraulic  press,  190,  191. 
Hydraulics,  182. 
Hydrometer,  the,  196. 
Hydrostatics,  182. 
Hypothesis,  5. 


INDEX. 


543 


Illumination,  law  of  intensity  of,  327. 

Images,  by  small  apertures,  296  ;  by  re- 
flection, 301  ;  by  two  mirrors,  304  ;  by 
concave  mirrors,  305  ;  by  convex  mir- 
rors, 306  ;  by  lenses,  325-327. 

Impenetrability,  62. 

Impulse,  92. 

Inclined  plane,  the,  153-155. 

Indestructibility,  63,  64. 

Induction,  magnetic,  426  ;  electrifica- 
tion by,  443  ;  electro-magnetic,  516. 

Induction  coil,  the,  5J8. 

Inertia,  30,  65,  66. 

Irradiation,  350. 

Isothermal  lines,  282. 

Isothermal  surfaces,  283,  284. 

Joule's  determination  of  the  mechani- 
cal equivalent  of  heat,  268. 

Kinematics,  13, 28. 
Knee,  the,  162. 

Law,  2,  3  ;  explanation  of,  5. 

Lenses,  321. 

Level,  of  liquids,  187,  188. 

Lever,  the,  144  ;  principle  of,  145  ;  work 
done  with,  147  ;  actual,  148. 

Leyden-jar,  the,  454,  455. 

Light,  293-369  ;  propagation  of,  295  ; 
velocity  of,  297  ;  reflection  of,  299  ; 
refraction  of,  310  ;  under  water,  315  ; 
loss  of.  by  multiple  reflection,  321 ;  de- 
composition of,  by  prisms,  328  ;  polar- 
ization of,  361-365. 

Lightning,  462-464. 

Liquids,  166;  properties  of,  174-200; 
buoyancy  of,  193. 

Machines,  142 ;  efficiency  of,  143 ;  the 

simple,  144. 
Magnetism,  419-434 ;  laws  of,  423,  425  ; 

the  earth's,  430  ;  applications  of,  432. 
Magnets,  artificial,  419,  420  ;  compound, 

420 ;  rolling  armature,  426  ;  proper- 
ties of,  421-428. 
Malleability,  169. 
Manometric  flames,  410. 
Mass,  11,  61  ;  measurement  of,  76-80  ; 

standard,  81 ;  center  of,  124. 
Matter,  9  ;  perception  of,  10  ;  kinds  of, 

10  ;  properties  of,  60  ;  constitution  of, 

67  ;  states  of,  166. 
Mechanical  advantage,  149. 


Mechanics,  142. 

Medical  electricity,  538. 

Metric  measures,  table  of,  540. 

Microphone,  the,  521. 

Microscope,  the,  354. 

Mirrors,  301-308  ;  magic,  309. 

Molecular  differences,  167. 

Molecules,  12 ;  as  distinguished  from 
atoms,  71 ;  spaces  between,  72 ;  size 
of,  74,  75. 

Momentum,  92. 

Morse  code  of  signals,  510. 

Motion,  14  ;  relative,  15  ;  direction  of, 
16  ;  uniform,  17  ;  uniformly  acceler- 
ated, 19,  20 ;  free,  31 ;  laws  of,  31,  87, 
102 ;  perpetual,  148. 

Motions,  composition  of,  21,  22  ;  result- 
ant of  uniform,  22 ;  parallelogram 
of,  23  ;  resolution  of,  26. 

Musical  scale,  the,  405. 

Naphtha-engine,  the,  290,  291. 
Newton's  Laws  of  Motion,  31,  87,  102. 

Ohm,  the,  480. 
Ohm's  law,  496. 
Organ-pipes,  397. 
Osmosis,  180,  222. 

Pendulum,  the,  132 ;  laws  of,  133 ;  ap 
plication  of,  to  clocks,  135. 

Perpetual  motion,  148. 

Phenomena,  2  ;  explanation  of,  5. 

Phonograph,  the,  413-416. 

Photography,  344. 

Photometry,  359. 

Physical  science  defined,  1,  6,  7. 

Pitch,  398. 

Plant  temperature,  274. 

Plumb-line,  the,  127. 

Points,  action  of,  in  electricity,  449. 

Polarization  of  light,  361-365. 

Porosity,  72-74. 

Position,  14  ;  change  of,  14. 

Potential,  436. 

Power,  101. 

Pressure,  law  of  transmission  of,  182 ; 
equal  transmission  of,  183 ;  due  to 
weight  of  liquid,  184  ;  intensity  of, 
185  ;  upward,  of  liquids,  186  ;  atmos- 
pheric, 201,  225  ;  influence  of,  on  fus- 
ing and  boiling  points,  254-258;  of 
vapor  below  the  freezing-point,  259; 
of  vapors,  266. 


544 


INDEX. 


Prisms,  320  ;  decomposition  of  light  by, 

328  •  Nicol's,  364. 
Projectiles,  123. 

Pulley,  the,  160,  161 ;  law  of  the,  162. 
Pump,  air,  the,  211 ;  the  lifting,  213, 

214  ;  the  force,  216. 

Quadrant  electrometer,  the,  495. 

Radiant  energy,  38.  294. 

Radiation,  of  heat,  279  ;  in  a  vacuum, 

280. 

Rainbow,  the,  367,  368. 
Reflection  of  light,  299  ;  total,  313,  314. 
Refraction  of  light,  310  ;  law  of,  310,  312. 
Resistance,  electrical,  480 ;  coils,  481  ; 

measurement  of,  483-486. 
Resonators,  404. 
Rest,  15. 

Screw,  the,  157-159  ;  endless,  the,  160. 

Siphon,  the:  218,  219. 

Siren,  the,  399-401.     „ 

Solar  ray,  effects  of,  342,  343. 

Solids,  166  ;  properties  of,  167. 

Sonometer,  the,  391. 

Sound,  370-418 ;  nature  of,  370 ;  velocity 
of,  376  ;  propagation  of,  378  ;  inter- 
ference of,  384 ;  reflection  of,  387  ; 
refraction  of,  388 ;  diffraction  of, 
389  ;  elements  of,  398. 

Sound-wave,  380-384. 

Space,  8  ;  location  of  bodies  in,  9. 

Specific  gravity,  195,  196. 

Specific  heat,  246. 

Spectroscope,  the,  338-342. 

Spectrum,  the,  328,  329. 

Speech,  409. 

Spring-balance,  the,  84. 

Stability,  128-131. 

Steam-engine,  the,  286-290. 

Stereopticon,  the,  353. 

Stereoscope,  the,  358. 

Storage-batteries,  534-536. 

Surface  tension,  175. 

Telegraph,  the  electro-magnetic,  507- 

514. 
Telegraphy,    duplex,    512;    multiplex, 

513  ;  submarine,  513. 


Telephone,  the,  519-521. 

Telescope,  the,  355. 

Temperature,  231 ;  rise  of,  produced  by 
heat,  232  ;  of  plants,  274. 

Temperature  compensation,  238. 

Theory,  5. 

Thermometer,  the,  235  ;  maximum  and 
minimum,  236;  wet  and  dry  bulb. 
264. 

j  Thermometer-scales,  235,  236. 
j  Timbre,  402. 
|  Time,  7  ;  measurement  of,  8. 

Toepler-Holtz  machine,  the,  450. 

Toggle-joint,  the,  162. 
I 

Unit,  of  force,  90  ;  of  energy,  95 ;  of 
work,  95,  96 ;  British  engineering,  of 
mass,  98  ;  British  engineering,  of 
work,  99  ;  British  engineering,  of 
energy,  99 ;  of  electrical  resistance, 
480. 

Units,  87-91  ;  distinguished  from  stand- 
ards, 88 ;  of  length,  time,  and  mass, 
89  ;  British  engineering,  98  ;  French 
engineering,  100  ;  thermal,  244. 

Vaporization,  249. 

Vapor  pressures,  266. 

Velocity,    17 ;    average,    18 ;    of   light, 

297  ;  of  sound,  376  ;  of  electricity,  504. 
Vibration,  372-374 ;  of  strings,  390 ;  of 

rods,  393;    of  plates,  395;    of  bells, 

395  ;  of  columns  of  air,  396. 
Viscosity,  172. 
Vision,  mechanism  of,  346. 
Visual  angle,  348. 

Voice,  the,  407,  408  ;  disorders  of,  409. 
Volt,  the,  493. 
Voltaic  cell,  the,  469^75. 

Water,  flow  of,  197;  in  the  soil,  198, 

199  ;  light  under,  315. 
Wedge,  the,  156. 
Weighing,  164. 
Weight,  48,  120 ;  above  and  below  the 

earth's  surface,  121  ;  of  gases,  200. 
Welding,  168  ;  electric,  532. 
Wheel  and  axle,  the,  151. 
Work,  28  ;  definition  of,  42  ;  unit  of,  95. 


PUBLICATIONS  OF  THE  AMERICAN  BOOK  COMPANY. 


Chemistry. 


Armstrong  and   Norton's  Laboratory   Manual   of 
Chemistry. 

By  JAMES  E.  ARMSTRONG  and  JAMES  H.  NORTON.  ...    50  cents. 

One  hundred  and  sixty-four  experiments,  or  a  year's  work,  clearly  though  briefly 
explained,  and  employing  simple  and  for  the  most  part  inexpensive  apparatus. 

Brewster's  First  Book  of  Chemistry. 

By  MARY-SHAW  BREWSTER 66  cents. 

A  course  of  experiments  of  the  most  elementary  character  for  the  guidance  of  chil- 
dren in  the  simplest  preliminary  chemical  operations.  The  simplest  apparatus  is  em- 
ployed. 

Clarke's  Elements  of  Chemistry. 

By  F.  W.  CLARKE $1.20. 

A  class-book  intended  to  serve,  not  only  as  a  complete  course  for  pupils  studying 
chemistry  merely  as  part  of  a  general  education,  but  also  as  a  scientific  basis  for  subse- 
quent higher  study. 

Cooley's  New  Elementary  Chemistry  for  Begin- 
ners. 

By  LE  ROY  C.  COOLEY 72  cents. 

This  is  emphatically  a  book  of  experimental  chemistry.  Facts  and  principles  are 
derived  from  experiments,  and  are  clearly  stated  in  their  order. 

Cooley's  New  Text-Book  of  Chemistry. 

By  LE  ROY  C.  COOLEY 90  cents. 

A  text-book  of  chemistry  for  use  in  high  schools  and  academies. 

Eliot  and  Storer's  Elementary  Chemistry. 

Abridged  from  Eliot  and  Storer's  Manual,  by  WILLIAM  RIPLEY 

NICHOLS,  with  the  co-operation  of  the  authors $1.08. 

Adapted  for  use  in  high  schools,  normal  schools,  and  colleges. 

Steele's  New  Popular  Chemistry. 

By  J.  DORMAN  STEELE,  Ph.  D $1.00. 

Devoted  to  principles  and  practical  applications.  Not  a  work  of  reference,  but  a 
pleasant  study.  Only  the  main  facts  and  principles  of  the  science  are  given. 

Stoddard's  Qualitative  Analysis. 

By  JOHN  T.  STODDARD,  Ph.  D 75  cents. 

An  outline  of  qualitative  analysis  for  beginners.  The  student  is  expected  to  make 
the  reactions  and  express  them  in  written  equations. 

Stoddard's  Lecture  Notes  on  General  Chemistry. 

Part    I.    Non-Metals $0.75. 

Part  II.    Metals i.oo. 

Designed  as  a  basis  of  notes  to  be  taken  on  a  first  course  of  experimental  lectures  on 
general  chemistry,  to  relieve  the  student  from  the  most  irksome  part  of  his  note-taking. 

Youmans's  Class-Book  of  Chemistry. 

By  EDWARD  L.  YOUMANS,  M.  D.     Third  edition.     Revised  and 

partly  rewritten  by  WILLIAM  J.  YOUMANS,  M.  D $1.22. 

Designed  as  a  popular  introduction  to  the  study  of  the  science,  for  schools,  colleges, 
and  general  reading.  With  a  colored  frontispiece  and  158  illustrations. 

Copies  mailed,  post-paid,  on  receipt  of  price.     Full  price-list  sent  on  application. 

AMERICAN   BOOK  COMPANY, 

NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO. 

t*68] 


PUBLICATIONS  OF  THE   AMERICAN   BOOK   COMPANY. 

Zoology  and  Natural  History. 

Cooper's  Animal  Life. 

By  SARAH   COOPER $1.25. 

Animal  life  in  the  sea  and  on  the  land.  A  zoology  for  young  people.  Especial  at- 
tention has  been  given  to  the  structure  of  animals,  and  to  the  wonderful  adaptation  of 
this  structure  to  their  habits  of  life. 

Holder's  Elementary  Zooiogy. 

By  C.  F.  HOLDER $1.20. 

A  text-book  designed  to  present  in  concise  language  the  life-histories  of  the  groups 
that  constitute  the  animal  kingdom,  giving  special  prominence  to  distinctive  character- 
istics and  habits. 

Hooker's  Child's  Book  of  Nature. 

Part  II.  Animals.     By  WORTHINGTON  HOOKER,  M.  D.    $0.44. 

While  this  work  is  well  suited  as  a  class-book  for  schools,  its  fresh  and  simple  style 
can  not  fail  to  render  it  a  great  favorite  for  family  reading. 

Hooker's  Natural  History. 

By  WORTHINGTON  HOOKER,  M.  D .    .    $0.90. 

For  the  use  of  schools  and  families.  Illustrated  by  three  hundred  engravings.  The 
book  includes  only  that  which  every  well-informed  person  ought  to  know,  and  excludes 
all  which  is  of  interest  only  to  those  who  intend  to  be  thorough  zoologists. 

Morse's  First  Book  in  Zoology. 

By  E.  S.  MORSE,  Ph.  D $0.87. 

Prepared  for  the  use  of  pupils  who  wish  to  gain  a  general  knowledge  concerning 
the  common  animals  of  the  country.  The  examples  presented  for  study  are  such  as 
are  common  and  familiar  to  every  school-boy. 

Nicholson's  Text-Book  of  Zoology. 

By  H.  A.  NICHOLSON,  M.  D .    .    $1.38. 

Revised  edition.  A  work  strictly  elementary,  designed  for  junior  students.  Illus- 
trated with  numerous  engravings.  It  contains  an  Appendix,  Glossary,  and  Index. 

Steele's  New  Popular  Zoology. 

By  J.  DORMAN  STEELE,   Ph.D.     ........    $1.20. 

This  book  proceeds,  by  natural  development,  from  the  lowest  form  of  organism  to 
man.  A  cut  is  given  of  every  animal  named,  since  a  good  picture  of  an  object  is  worth 
more  than  pages  of  description. 

Tenney's  Elements  of  Zoology. 

By  SANBORN  TENNEY,  A.  M $1.60. 

Illustrated  by  seven  hundred  and  fifty  wood  engravings.  It  gives  an  outline  of  the 
animal  kingdom,  and  presents  the  elementary  facts  and  principles  of  zoology. 

Tenney's  Natural  History  of  Animals. 

By  SANBORN  TENNEY  and  ABBY  A.  TENNEY.     .     .     .     $1.20. 

A  brief  account  of  the  animal  kingdom,  for  the  use  of  parents  and  teachers.  Illus- 
trated by  five  hundred  wood  engravings,  chiefly  of  North  American  animals. 

Copies  mailed,  post-paid,  on  receipt  of  price.  Complete  price-list  sent  on  applica- 
tion. 

AMERICAN   BOOK  COMPANY, 

NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO. 


PUBLICATIONS  OF   THE   AMERICAN   BOOK  COMPANY. 

Geology. 

Andrews's  Elementary  Geology. 

By  E.  B.  ANDREWS,  LL.  D $1.00. 

This  book  is  designed  for  students  and  readers  of  the  Interior  States,  and  therefore 
has  its  chief  references  to  home  geology.  The  scope  is  limited,  to  adapt  it  to  beginners. 

Dana's  Geological  Story  Briefly  Told. 

By  JAMES  D.  DANA,  LL.  D $1.15. 

With  numerous  illustrations.  An  introduction  to  geology  for  the  general  reader, 
and  for  beginners  in  the  science.  It  contains  a  complete  alphabetical  index  of  subjects. 

Dana's  Manual  of  Geology. 

By  JAMES  D.  DANA,  LL.  D. $3.84. 

This  is  a  treatise  on  the  principles  of  the  science  adapted  to  the  wants  of  the 
American  student,  with  special  reference  to  American  geological  history.  The  illus- 
trations are  numerous,  accurate,  and  well  executed. 

Dana's  New  Text-Book  of  Geology. 

By  JAMES  D.  DANA,  LL.  D $2.00. 

On  the  plan  of  the  Manual,  designed  for  schools  and  academies.  The  explanations 
are  simple,  and  at  the  same  time  complete. 

Le  Conte's  Compend  of  Geology. 

By  JOSEPH  LE  CDNTE $1.20. 

A  book  designed  to  interest  the  pupil,  and  to  convey  real  scientific  knowledge.  It 
cultivates  the  habit  of  observation  by  directing  the  attention  of  the  pupil  to  scientific 
phenomena. 

Nicholson's  Text-Book  of  Geology. 

By  H.  A.  NICHOLSON $1.05. 

This  presents  the  leading  principles  and  facts  of  geological  science  within  as  brief 
a  compass  as  is  compatible  with  clearness  and  accuracy. 

Steele's  Fourteen  Weeks  in  Geology. 

By  J.  DORMAN  STEELE,  Ph.  D $1.00. 

Designed  to  make  science  interesting  by  omitting  those  details  which  are  valuable 
only  to  the  scientific  man,  and  by  presenting  only  those  points  of  general  importance 
with  which  every  well-informed  person  wishes  to  be  acquainted. 

Williams's  Applied  Geology. 

By  S.  G.  WILLIAMS $1.20. 

A  treatise  on  the  industrial  relations  of  geological  structure,  and  on  the  nature,  oc- 
currence, and  uses  of  substances  derived  from  geological  sources.  It  gives  a  connected 
and  systematic  view  of  the  applications  of  geology  to  the  various  uses  of  mankind. 


Copies  mailed,  post-paid,  on  receipt  of  price.     Full  price-list  sent  on  application. 

AMERICAN   BOOK  COMPANY, 

NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO. 

1*72] 


PUBLICATIONS   OF   THE   AMERICAN   BOOK  COMPANY. 

Astronomy. 

Bowen's  Astronomy  by  Observation. 

By  ELIZA   A.  BOWEN $1.00. 

An  elementary  text-book  for  high  schools  and  academies,  based  on  the  most  practi- 
cal and  interesting  method  of  studying  the  subject — that  of  observation. 

Gillet  and  Rolfe's  First  Book  in  Astronomy. 

By  JOSEPH  A.  GILLET  and  N.  J.  ROLFE $1.00. 

This  book,  while  intended  for  junior  classes,  is  by  no  means  primary  or  elementary 
It  is  designed  as  a  brief  course,  to  serve  as  a  foundation  for  more  extended  study. 

Gille;;  and  Rolfe's  Astronomy. 

By  JOSEPH  A.  GILLET  and  N.  J.  ROLFE $1.40. 

This  book  has  been  prepared  by  practical  teachers,  and  contains  nothing  beyond  the 
comprehension  of  the  student  of  a  high  school  or  a  seminary. 

Kiddle's  Short  Course  in  Astronomy. 

By  HENRY  KIDDLE,  A.  M.     Fully  illustrated.     .     .     .     $0.65. 

This  is  a  short  course  in  Astronomy  and  the  use  of  the  globes.  In  mechanical 
execution  it  is  unsurpassed. 

Kiddle's  New  Elementary  Astronomy. 

By  HENRY  KIDDLE,  A.  M $1.08. 

A  new  manual  of  the  elements  of  Astronomy,  descriptive  and  mathematical,  com- 
prising the  latest  discoveries  and  theoretical  views,  with  directions  for  the  use  of  globes, 
and  for  studying  the  constellations. 

Lockyer's  Elementary  Astronomy. 

By  J.  N.  LOCKYER,  F.  R.  S $1.22. 

Accompanied  with  numerous  illustrations,  a  colored  representation  of  the  solar, 
stellar,  and  nebular  spectra,  and  Arago's  celestial  charts  of  the  Northern  and  Southern 
Hemispheres.  Especially  adapted  to  the  wants  of  American  schools. 

Ray's  New  Elements  of  Astronomy. 

Revised  edition.     By  S.  H.  PEABODY $1.20. 

The  elements  of  Astronomy  with  numerous  engravings  and  star  maps.  The  author 
has  restricted  himself  to  plain  statements  of  the  facts,  principles,  and  processes  of  the 
science. 

Steele's  New  Descriptive  Astronomy. 

By  J.  DORMAN  STEELE,  Ph.  D $1.00. 

This  book  is  not  written  for  the  information  of  scientific  men,  but  for  the  inspiration 
of  youth.  The  author  has  sought  to  weave  the  story  of  those  far-distant  worlds  into  a 
form  that  may  attract  the  attention  and  kindle  the  enthusiasm  of  the  pupil. 


Copies  mailed,  post-paid,  on  receipt  of  price.     Full  price-list  sent  on  application. 

AMERICAN   BOOK  COMPANY, 

NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO. 

[*73] 


Physical   Geography. 


In  addition  to  the  series  of  Political  Geographies  published  by 
the  American  Book  Company,  their  list  includes  the  following  standard 
and  popular  text-books  on  Physical  Geography  : 

APPLETONS'  PHYSICAL  GEOGRAPHY. 

Large  4to $1.60 

Prepared  by  a  corps  of  scientific  experts  with  richly-illustrated  engravings, 
diagrams,  and  maps  in  color,  and  including  a  separate  chapter  on  the 
geological  history  and  the  physical  features  of  the  United  States. 

CORNELL'S  PHYSICAL   GEOGRAPHY. 

Large  4to $1.12 

Revised  edition,  with  such  alterations  and  additions  as  were  found  necessary 
to  bring  the  work  in  all  respects  up  to  date. 

ECLECTIC  PHYSICAL  GEOGRAPHY. 

i2mo $1.00 

By  RUSSELL  HINMAN.  A  new  work  in  a  new  and  convenient  form.  All 
irrelevant  matter  is  omitted  and  the  pages  devoted  exclusively  to 
Physical  Geography  clearly  treated  in  the  light  of  recent  investiga- 
tions. The  numerous  charts,  cuts,  and  diagrams  are  drawn  with 
accuracy,  fully  illustrating  the  text. 

GUYOT'S   PHYSICAL  GEOGRAPHY. 

Large  4to $1.60 

By  ARNOLD  GUYOT.  Revised,  with  new  plates  and  newly-engraved  maps.  A 
standard  work  by  one  of  the  ablest  of  modern  geographers.  All  parts 
of  the  subject  are  presented  in  their  true  relations  and  in  their  proper 
subordination. 

MONTEITH'S  NEW  PHYSICAL  GEOGRAPHY. 

4to       $1.00 

A  new  and  comprehensive  work,  embracing  the  results  of  recent  research  in 
this  field,  including  Physiography,  Hydrography,  Meteorology,  Ter- 
restial  Magnetism,  and  Vulcanology.  The  topical  arrangement  of 
subjects  adapts  the  work  for  use  in  grammar  grades  as  well  as  for  high 
and  normal  schools. 

Any  of  the  above  books  will  be  mailed  ^postpaid,  on  receipt  of  price.     Full 
price-list  of  books  on  all  subjects  for  all  grades  "will  be  sent  on  application. 


AMERICAN  BOOK  COMPANY, 

NEW  YORK          .-.          CINCINNATI  .-.  CHICAGO 


PUBLICATIONS   OF   THE  AMERICAN   BOOK   COMPANY. 


Geometry. 


DAVIES'S   GEOMETRIES.     By  CHAS.  DAVIES,  LL.  D. 

Elementary  Geometry   and   Trigonometry.       i2mo,  cloth, 

324  pages $1.00 

Legendre's    Geometry   and   Trigonometry.     Revised  by  I. 

H.  VAN  AMRINGE.     8vo,  sheep.     512  pages       .        .        .  $1.60 

THE  SAME.     Part  I,  Geometry  only.     291  pages   .         .         .  $1.25 

Davies's  Legendre's  Geometry  is  an  entirely  new  edition,  made  to  conform 

with  latest  and  best  methods. 

ECLECTIC  SCHOOL  GEOMETRY.  (Elementary.)  By  E. 

W.  EVANS,- A.  M.     i2mo,  cloth.     155  pages     .        .     60  cents 

A  revision  of  Evans's  School  Geometry  by  J.  J.  Burns,  M.  A.,  especially 

adapted  to  high  schools  by  the  addition  of  numerous  exercises  and  original 

demonstrations. 

HUNTER'S    Elements    of   Plane    Geometry.         By  THOMAS 
HUNTER,  Ph.  D.     I2mo,  cloth.     132  pages        .         .      60  cents 
This  volume  is  intended  only  for  beginners— for  those  who  are  preparing 
for  college,  and  for  intermediate  and  high  schools  generally. 

PECK'S  ANALYTICAL    GEOMETRY.     By  WM.  G.  PECK, 

Ph.D.     I2mo,  cloth.     212  pages $1.25 

A  treatise  on  analytical  geometry,  with  applications  to  lines  and  surfaces 
of  the  first  and  second  orders. 

PECK'S   DETERMINANTS.     By  WM.  G.  PECK,  Ph.  D.     I2mo, 

cloth.     70  pages 60  cents 

Designed  as  an  introduction  to  a  course  of  modern  analytical  geometry. 

RAY'S    PLANE    AND    SOLID    GEOMETRY.     i2mo,  cloth. 

276  pages 70  cents 

Written  for  Ray's  Mathematical  Course  by  ELI  T.  TAPPAN,  M.  A. 

ROBINSON'S  NEW  GEOMETRY  AND  TRIGONOM- 
ETRY. 8vo,  calf.  453  pages $1.60 

Embracing  plane  and  solid  geometry,  and  plane   and  spherical  trigo- 
nometry, with  numerous  practical  problems. 

SPENCER'S  INVENTIONAL  GEOMETRY.  (Science 
Primer  Series.)  By  WM.  GEO.  SPENCER.  i8mo,  flexible  cloth. 

97  pages 35  cents 

Introduces  the  beginner  to  geometry  by  putting  him  at  work  on  problems 

which  exercise  his  inventive  and  constructive  faculties. 

Copies  of  the  above  mailed,  post-paid,  to  any  address  on  receipt  of  price.     Send  for 
full  descriptive  catalogue  of  text-books  in  all  departments  of  higher  mathematics. 

AMERICAN    BOOK    COMPANY, 

NEW  YORK          •:•          CINCINNATI          •:•          CHICAGO 
[*«] 


PUBLICATIONS  OF  THE  AMERICAN   BOOK   COMPANY. 

GENERAL  HISTORY. 

THALHEIMER'S  GENERAL  HISTORY. 

i2mo,  448  pp.     Half  roan,  illustrated  .  .  .  $1.20 

Extreme  brevity  has  here  been  combined  with  a  lively  and  simple  narrative, 
such  as  might  supply  the  present  need  of  young  pupils  while  affording  a  sym- 
metrical plan  for  the  research  of  older  ones. 

SWINTON'S  OUTLINES  OF  HISTORY. 

isrno,  500  pp.     Cloth         .  .  .  .  .  .  $i-44 

Ancient,  Mediaeval  and  Modern,  with  special  reference  to  the  History  oi 
Mankind.  Its  anatomical  synopses,  its  maps  showing  the  political  divisions  at 
the  great  epochs,  its  collateral  information,  its  surveys  of  the  great  events,  dis- 
tinguished men,  and  important  discoveries.furnish  in  an  entertaining  style  just 
what  is  valuable  to  the  beginner  of  the  study  of  history. 

LORD'S   POINTS  OF  HISTORY. 

lamo,  300  pp.     Cloth          ......  $1.00 

The  salient  points  in  the  history  of  the  world  arranged  catechetically  for 
class  use  or  for  review  and  examination  by  teacher  or  pupil. 

OILMAN'S  FIRST  STEPS   IN   GENERAL  HISTORY. 

i8mo,  385  pp.     Cloth        .  .  .  .  .  -75  cents 

A  suggestive  outline  of  great  compactness.  Each  country  is  treated  by  itself, 
and  the  United  States  receives  special  attention.  Frequent  maps,  contempo- 
rary events  in  tables,  references  to  standard  works  for  fuller  details,  and  a  mi- 
nute index  constitute  the  "  Illustrative  Apparatus."  The  style  is  surprisingly 
vivid  and  at  times  even  ornate. 

FISHER'S    OUTLINES    OF    UNIVERSAL    HISTORY. 

8vo,  690  pp.     Cloth  ......  $2.40 

This  work,  designed  as  a  text-book  and  for  private  reading,  is  a  clear  and 
condensed  narrative,  brought  down  to  the  present  year,  comprising  not  only  a 
record  of  political  events,  but  also  a  sketch  of  the  progress  of  literature,  art  and 
science  from  the  beginning  of  history  to  the  present  time. 

BARNES'S  GENERAL  HISTORY  OF  THE  WORLD. 

i2mo,  600  pp.     Cloth         ......  $1.60 

A  complete  outline  of  the  world's  history.  Some  of  the  prominent  features 
comprise :  blackboard  analysis  ;  summaries  to  assist  in  review  ;  lists  of  reading 
references ;  colored  maps  ;  scenes  in  real  life  ;  chapters  on  civilization  ;  gene- 
alogical tables  ;  foot-notes  ;  chapters  devoted  to  the  rise  of  modern  nations. 

The  pupil  insensibly  acquires  a  taste  for  historical  reading  and  forgets  the 
tediousness  of  the  ordinary  lesson  in  perusing  the  thrilling  story  of  the  past. 

APPLETONS'  SCHOOL  HISTORY  OF  THE  WORLD. 

8vo,  491  pp.      Cloth  .  .  .  .  .  .  $1.22 

From  the  earliest  ages  to  the  present  time.  A  clear,  fresh,  carefully  arranged 
and  condensed  work,  beautifully  illustrated.  It  treats  ancient  civilization  in 
the  light  of  the  most  recent  discoveries.  The  whole  history  of  the  past  con- 
densed into  a  moderate-sized  volume  that  can  be  readily  mastered  in  the  ordi- 
nary school  year. 

Copies  of  these  or  any  of  the  publications  of  the  American  Book  Company  for 
the  use  of  teachers  or  school  officers,  or  for  examination  with  a  view  to  intro- 
duction^ will  be  sent  by  mail ',  postpaid,  on  receipt  of  the  list  or  introduction  price. 

AMERICAN    BOOK    COMPANY, 

NEW  YORK  /.  CINCINNATI  .'.  CHICAGO. 

C*39] 


PUBLICATIONS  OF  THE  AMERICAN  BOOK  COMPANY. 

History — England  and   France. 


BERARD'S  SCHOOL  HISTORY  OF  ENGLAND. 

i2mo,  470  pp.     Cloth         .  .  .  .  .  .  $1.20 

The  social  life  of  the  English  people  is  felicitously  interwoven  with  the  civil 
and  military  transactions  of  the  country.  The  nation's  religion,  literature, 
science,  art  and  commerce  occupy  a  prominent  place  in  the  book. 

DICKENS'S  CHILD'S  HISTORY  OF  ENGLAND. 

i6mo,  308  pp.     Half  Leather     .  .  .  .  .60  cents 

Related  in  a  charming  narrative  style,  so  that  it  reads  to  the  child  like  a 

story.    The  events  are  so  vividly  portrayed,  and  in  so  interesting  a  manner 

that  even  a  child  without  the  desire  to  learn  is  led  to  read  on  from  sheer 

interest. 

LANCASTER'S   MANUAL    OF    ENGLISH    HISTORY. 

I2mo,  324  pp.    Cloth        -.-,..-.  .  .  .  $1.00 

A  brief  and  practical  book.    Though  short,  it  is  not  a  bare  and  uninteresting 

outline,  but  contains  enough  of  explanation  and  detail  to  make  intelligible  the 

cause  and  effect  of  events.    Their  relations  to  the  history  and  development  of 

the  American  people  are  made  specially  prominent. 

MORRIS'S  HISTORY  OF  ENGLAND. 

I2mo,  533  pp.     Cloth        -.  .  .  .  .,          .  $1.00 

In  this  book  the  events  of  each  reign,  grouped  according  to  their  order  and 

importance,  are  placed  at  the  beginning  of  each  chapter,  and  the  outline  thus 

given  is  filled  up  in  detail.    A  chapter  on  the  social  condition  of  the  people 

is  given  at  the  end  of  each  period. 

THALHEIMER'S  HISTORY  OF  ENGLAND,  s 

12010,  288  pp.     Cloth,  illustrated         .  *  ,         .         ^rX^i.oo 

A  compact  volume,  comprehensive  in  scope,  but  sufficiently  brief  to  be  com- 
pleted in  one  school  term.  Its  statements  of  historical  facts  are  based  upon  the 
studies  of  the  most  recent  and  reliable  authorities.  The  maps  are  superior  in 
fullness,  accuracy  and  beauty. 

BARNES'S   BRIEF  HISTORY  OF   FRANCE. 

i2mo,  330  pp.     Cloth         .  .  .  .  •        ..  «    '        $1.00 

This  book  is  primary  in  matter  and  manner  of  treatment.  Especially  inter- 
esting are  the  chapters  on  manners  and  customs  of  the  people  at  different 
periods,  and  the  linking  of  events  by  tracing  cause  and  effect. 

YONGE'S   HISTORY   OF   FRANCE.     (Primer  Series.) 

i8mo,  122  pp.     Flexible  cloth    .  .  .  .  -35  cents 

With  maps  of  France  showing  the  provinces  and  the  departments.  A  short 
but  comprehensive  history  of  France,  designed  for  use  in  schools  where  but 
little  time  is  devoted  to  this  subject  or  as  a  reference  book.  Topical  head- 
ings are  placed  at  the  beginning  of  the  paragraphs. 


Copies  of  these  or  any  of  the  publications  of  the  American  Book  Company  for 
the  use  of  teachers  or  school  officer s^  or  for  examination  with  a  view  to  intro- 
duction, will  be  sent  by  mail \  postpaid,  on  receipt  of  the  list  or  introduction  price. 

AMERICAN    BOOK    COMPANY, 

NEW  YORK  .'.  CINCINNATI  .'.  CHICAGO. 

[*4o] 


UNIVERSITY  OF  CALIFORNIA  LIBRAR5 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


<3  1914 
6  1915' 


DEC  3   1917 

.'*  281918 
MAR   4  U18 
FEB  18  1919 

SEP  1    ISJ9 


.  is  » 

SEP  1 


JULli 


